I'm quite a noob still, but in my effort to look for some turn overbet spots with the solver, it seems to me like the range for value tends to actually not be very polarized. I'm also aware that obviously the turn itself needs to favor your range.

Sometimes it'll use a hand like bottom set on 567T but often it just uses weak Tx, a type of hand that I assume likes to bomb it for equity denial. Is this what I look for across all turns? Is there any other patterns that help you choose appropriate combos for it, or any nice logical way to build the ranges?

When I started looking into it I figured it would be extremely polarized, using something like the flopped straight on the 567 board, but the solver actually doesn't seem to like overbetting the nuts

The basic idea is that on dynamic boards, your opponent is heavily incentivized to not slowplay. This means that if they check or call, they are heavily capped. They almost always have some sort of weak pair or draw.
What this all means is that, if the turn bricks, your TPWK are actually very close to beating most of your opponent's range. However, they are still very vulnerable, your opponent has plenty of draws and pairs that can 2pair. So they make a lot of sense to overbet, despite not being that strong.
Just like we can attack our opps capped range on the turn, he can do so too after we check the turn, and thus, if we had an invulnerable hand, it would make sense to check it to "protect" our weak capped check range. This is why it's not OBing your flopped straight