How to manually update a very old version?

A few comments on your query:

First, Brave has Chromium (admittedly an aggressively de-Googled Chromium) at its core. Chromium has cut off support for older operating systems (not just Windows…) This dictates Brave’s behavior as to what operating systems are supported.

Second, some non-Chromium browsers continue to be updated on old(er) operating systems. That’s not … forever.

Third, Windows 10 is - emphatically - not “better” than earlier versions of Windows. It is more-or-less current, and near-term, Microsoft continues to support it. Chromium and Chromium-based browsers are - for now - supported on Windows 10, but for many folks, that’s not a sufficient reason to abandon an earlier no-longer-supported operating system.

Forth, lack of security updates is a compelling reason to no longer use earlier operating systems on-line.

Which leads to - fifth, you might consider a dual-boot arrangement with your current hardware, installing a version of linux in addition to Windows 7. That’s what I (and many other users) have done. It’s not for everyone, any more than the sweeping (and wrong) assertion that ‘Windows 10 is better.’ I’ll not recommend a specific linux version other than to note: recent announcements from Red Hat suggest long-term support for individual users may be halted.

Sixth (and last), this is a Brave Community support forum. Here’s the Brave support page for installing Brave on linux

One possible deal-breaker for you: Brave on linux requires a 64-bit processor. If your laptop has a 32-bit processor…