>>96727804 (OP)
I love mecha (and tanks, and hover tanks, and power armor, and... wel, you get it) but I've never seen a dedicated mecha system that worked well. However, there are a few scifi systems that take on mecha pretty well.
Traveller I think does it the best. CT didn't explicitly have mecha rules but it was easy enough to use vehicle rules and extrapolate. The elegant thing it did was that the larger the size difference was between to the easier it was to target the larger and the harder it was to target the smaller. Fan made mecha accessory books for traveller have been made for a long time. (I even heard from a source I believe that Battletech started out as a Traveller homebrew.)
The WEG Star Wars had walkers and even expanded them. Lets be honest, a paint job and some new plots and Star Wars could easily be a mecha anime. As it is, it's the most popular unsupported TTRPG and for good reason. A little work and you got yourself a banger space opera with mecha.
A new kid on the block but one I love is Black Star. It has a third party mecha book called Mecha Star that's been well loved at my table.I'm sure there's similar things with other scifi games but that's where I'd point you first.