My understanding is that while Russia annexed Kherson, they did not annex Kharkhiv.

I'm very confident the parts of Ukraine that have been trying to leave since 2014 mostly want to leave. I know ethnic Russians and Russian speakers are most heavily concentrated in the east, not just in the pre-war separatist regions but surrounding them, too. I'm sure war breaking out caused a lot of people who were on the fence to pick a side, and I can imagine someone who speaks Russian at home but wasn't radical enough to be part of a pre-war separatist movement throwing in with the much stronger country, that speaks their language, that doesn't have troops running around with neo-Nazi patches and flags.

all data I have seen (I can dig some up if you'd like-do not have it to hand) indicates strong support for the Ukrainian govt against the invasion

What I've seen is breakdowns of ethnic Russians and Russian speakers, which are predominantly in the east. I've also seen pre-war election results that show these eastern regions disagree with western Ukraine on national politics.