You might be out of luck, I'm afraid.
The majority of modern browsers (including Chrome, Slimjet, Vivaldi and the latest version of Edge) are based around the Blink browser engine (which, in turn, is part of the Chromium project). When, for example, I visit a site that detects which web browser I'm using, it doesn't 'see' my actual web browser, Slimjet 31.02.0, but only 'sees' Chromium 90.0.4430.93, leading it to think that I'm using Chrome (since that's by far the most popular browser which would be detected in such a way).
So any Chrome/Blink-based browser that's capable of running under Vista is going to be detected in exactly the same way. (i.e. as out of date and potentially putting your security at risk).
The only other widely-used browser engine is Gecko, which powers Firefox and those browsers which have been forked from it (such as K-Meleon, SeaMonkey and Waterfox). So if you use any Vista-compatible Gecko-based browser, it's likely to be 'seen' as an older version of Firefox.
You could still try an older version of Firefox though. (The last version to run under Vista was 52.9.0, downloadable from here:
http://ftp.mozilla.org/pub/firefox/releases/52.9.0esr/win32/en-GB/Firefox%20Setup%2052.9.0esr.exe ). However I suspect that it will still be seen as 'out of date' by your energy supplier's server.
You could also try Internet Explorer (which will be on your laptop anyway and powered by the Trident browser engine) but, once again, it's likely that your energy supplier won't permit you to use it.
Your energy supplier is legally-obliged to ensure that your online transactions with them are kept secure, meaning that they
must only allow data to pass via a secure operating system and an equally secure web browser. So you could well be out of luck in trying to use Vista to manage your account online. (Microsoft's main support for Vista ended 9 years ago, with residual support ending 4 years ago).
It might be time to bit the bullet and get a Windows 10 laptop. I paid £200 for the refurbished one that I'm using now, with loads of RAM, a fast processor and a solid state drive but you can get a decent Windows laptop for not much more that half that sum if you're prepared to accept a traditional hard drive and a bit less RAM. (Let me know if you need advice on where to buy from).
[PS: If you've got a smartphone, remember that you an also access your energy account that way, avoiding the problems of using Windows-based systems altogether].