camlorn is wrong, you could do it. I won't tell you how because I really do think you should move on from BGT, but the answer of you probably can't do it is simply incorrect

The simple answer is that it depends on your game
If you are using that PHP script, you can use ssmtp for your mail. You can have your Gmail or any other mail service for sending mail to the desired mail address

Yeah, my annoyance was with the "I won't tell you how, because you should move on from BGT..." idea. Seriously, why bother posting then? It's not constructive, it's absolutely not helpful, and it's a waste of time to read. Good for you, you know how to do it. Isn't the entire point of this forum to share knowledge and learn from the experiences of others, not make it a superiority complex?

LOL, I gave up on this dev room as a source of reliable information a long time ago, let alone asking a question myself. Because the pattern is always the same: people hijack the question by telling you what not to do instead of what to do, asking you to not use the technology you are asking about because they know so much better than everyone else (and not just in tech), and never missing a chance to flaunt their credentials, whether it's a computer science degree or a senior software engineering position. Yeah, no thanks, I think I'll just "google it", which I'm sure you're happy to hear since that was this group's favorite mantra for a while, if I remember correctly. And no, I don't buy the "more experience in life means more knowledge" argument. As valid as it may be, humility is a thing. There are ways to approach things. Honestly, I am someone who is currently pursuing a computer science degree and wishes to become a software engineer and possibly a senior one one day though I know I can never reach the level of our current resident expert, and honestly, I'm fine with that. Because I dread ever, ever having these qualities and attitudes towards people, especially those who may not have as much experience and need help. Literally, if this is how some people turn out when becoming coders, I want no part of it. I am someone who likes to help out wherever possible, whatever is within my capacity I try to do. Bringing smiles of satisfaction on people's faces brings me satisfaction for myself. This is partly why I started building software in the first place. If this is the cost, then there is no point for me anyway. So yeah, I am very cautious of this stuff. If I ever turn into one of these people in like 10 years, then I hope I get shut down and told off for that and quit frequenting any forums of this nature, and do my own thing. Because clearly, helping the community out at large in a constructive fashion is not something I can do.

If BGT supports use of the run function under wine, it becomes much simpler by calling external APIs with curl.
If JSON is needed, you can implement JSON parsers manually, make a valid request in advance and filling missing informations with string joins, or you could wrap a JSON parsing library in custom DLL. Though I would prefer the second method if all you need is a single API call.
If BGT doesn't support run under wine, you can wrap libcurl.dll in your server program or more effectively, setup an HTTP endpoint that BGT programs can connect and call external APIs indirectly threw that endpoint.
Hope this helps.

Yeah accept what Camlorn and crew does not a one-time occurrence. Also no I don't think just flat-out ignoring is the solution. How would you know if this "People get frustrated and move on" doesn't mean move on from programming entirely because their interest and motivation has died off after lack of support from the community? Some prefer to learn from experience. If they want to pick up BGT and possibly regret their choices later on their own terms, then so be it. I would go for the gentle nudge plus help approach. If you have something actually productive to say that would add to the discussion at hand, like if you have knowledge about the BGT question in this case, then contribute, and then gently warn them by saying hey, just so you know, it's not a very good idea to use BGT nowadays and here's why. But if you come in here just to say don't use this, or google it, and don't really add anything else to the discussion at hand then yeah I agree by all means please ignore and skip past the topic because you resisting your temptation will save everyone a whole lot of frustration and annoyance, particularly the OP I'm guessing.
And No, I don't buy the "but oh mah gooood I covered this so many times before so now I won't bother now but drop one very unhelpful sentence without context and you can google or search the forum for the rest" argument, for reasons that have been discussed above and many times before, E.g. the user being new to the forum.
Even if that is all you have to say, keep it to a minimum for exceptional cases where you think it absolutely urgently 100% has to be said, not over and over and over, and phrase it in a way where it doesn't sound arrogant and superior and honestly dickish;because it is already by nature going to be 80%unproductive to the discussion at hand then you add 18.85% more to that or something with this behavior. Which is the case in this room most of the times.

What I used to do back when I used BGT was a code system.
When you create an account, you were assigned a recovery code that was hashed. You would be asked to store said code in a secure place. The code consisted of letters, numbers, and special characters.
If you forgot the password, you would then be required to enter said recovery code. If you got it correct, you could create a new password. Otherwise you would have to talk to a member of staff. Staff did not have access to recovery codes, as that was the player's job, but they could reset your password to a temporary one, which you would change on your own. For instance, it may be reset to something like password, or changeme.
Before you go, this is good, there are major drawbacks to this system.
1. The big one is security. "What do you mean, you said the code was hashed." Yes, but here is the problem. Someone gets a hold of that code, and boom. Instant access to everything on that account.
2. Limited verification. You could ask to make sure the e-mail on the account matches the e-mail the person is providing, but it's yet another flaw. If the person knows your e-mail, there's a higher chance of that player gaining access.
3. It falls all on you. There is no external verification involved. You could put yourself behind a wall and say, "I'm not responsible if your code gets leaked." But that wall can be easily broken, because in a way, you are responsible for making a system that allowed such casualties to happen, probably on a very frequent basis.

A better system is to send a verification code to an e-mail, like others recommended in this post. If someone gains the code, that's not necessarily your fault. That's on the user for choosing such a weak password on their account, e-mail account, or both. That's out of your control. You've done your job by sending them a verification code. They receive it, they enter it, bada bing bada boom.
Also, in full agreement with Quin here. You either help, or shut up and continue drinking your beverage or eating your snack, or whatever you are doing.

You know, the developers room constant response of fuck you, I know how to do something in bgt but I won't tell you how, is the reason why I made bgtGPT  in the first place. Then openAI broke custom BGT's and heavily limited their base knowledge a little bit and it nose dove into the ground, so I just stopped updating it and fixing it. But if people keep acting like this i very well might just, recreate it.

Yeah, except not a lot of people complain about excluding Manamon which is made in BGT, or Crazy Party back when it was in BGT. There were not many frequent complaints about STW being in BGT, almost no one had problems excluding that either.