Time zone does hurt. I think I would proactively communicate "willing to work on these timezones schedules" during the application.

Most remote friendly organizations have a good amount of flex in the workdayb hours, as long as a few daily hours overlap for everyone. This means it's often possible to meet half way, where I'm working earlier or later than is strictly ideal for y area, but my day overlaps substantially with the team.

It is a hard time to get hired, right now. It should get better once the regulation and budget cuts in US politics settle down a bit.

For remote jobs, I've still gotten most of my jobs through personal references from people I know, just like before remote work was so popular.