How much did Schwarzenegger’s tenure as governor hurt the gop there
Not as much as Pete Wilson's did.
I don’t think he can be blamed as much as he has been as the gop was still competitive state wide their until 2008(senate elections had incumbents and those are usually easily won if they are popular)
It seems like the really collapsed during Bush’s 2nd term
Well, in some 2010 races they did also well. Kamala Harris won her first term as attorney general by about 1% (46-45%).
The new primary system is certainly not helping the GOP either because they mostly get to a run-off if the Democrat is an incumbent. On the state level, it also depends on the person. I think Kevin Faulconer would be competative in a year with a bad national climate for Democrats.