Yes, it won't suddenly stop working. It will just get more and more out-of-date and struggle with new protocols and security systems that didn't exist when it was last up-dated.

The various forks of Firefox may well still support Windows 7, for instance there's one called R3dfox that also still supports Vista and there's at least one that claims to work on XP.

I have seen some threads here in last months of some sites or such that claims Firefox 115 is too old or need a newer version to work properly as it may not realize that the user may be using Fx 115 ESR and not the Fx 115.0 Release. Though Firefox 115 ESR is based on the Fx 115 Release but only updated with security/stability fixes and no new features. Even after Firefox 115 ESR is finally made EOL it will still work. However websites and such still work properly may be an issue.

Normally the ESR channel versions are meant more for Enterprise users in mind as they like longer term stability however Mozilla has used them to support a EOL OS's for a longer time. For example Mozilla supported Windows XP/Vista for over two years longer compared to Chrome/Chromium based browsers with Firefox 52 ESR (till 52.9.0esr).

https://support.mozilla.org/en-US/kb/firefox-users-windows-7-8-and-81-moving-extended-support

https://whattrainisitnow.com/release/?version=esr

We decided to extend support for ESR 115 only on Windows 7-8.1 and macOS 10.12-10.14 up to March 2025. We will re-evaluate this decision in early 2025 and announce any updates on ESR 115's end-of-life then.

Pretty much every other major web browser (besides say SeaMonkey) has dropped support of Windows 7, 8, 8.1 back in Jan/Feb of 2023.

In the long run, besides updating to Windows 10 or 11, if you are adventurous/technical enough you could even consider trying to dual boot with a light Linux distro in order to use current Firefox versions. I do suggest to use say XFCE over say the heavier GNOME and KDE for desktop.

I resisted the temptation to mention Linux but thought the same.

However my choice of desktop would be Mate as it's a good compromise between system load (it works fine on my Pentium 4) and functionality and would also feel more familiar to somebody coming from Windows. In fact something like the Mate edition of Linux Mint would be less of a shock to somebody coming from Windows 7 than Windows 10 or 11 would be.