What options does an Indian engineer stuck in the green card backlog have? Do they perpetually continue renewing their H1-B? Does this mean that they are somewhat limited in terms of being able to switch jobs?
It depends on where you are in the green card process. If you are somehow in the last stage, with a pending I-485 application, you do have job flexibility (known as portability). Short of that, the only way to get out of this awful loop is to pursue a self-sponsored EB1A green card, but the standard is high as you probably know.
I am moving to either London or Canada. Applying for express entry next year. If I can get my Canadian residency by 2024, then I'll move to Canada. Otherwise, apply for a transfer to the London office.
Sometime, in the future, if I can have $800K to spare, then will go for EB-5. Although, this may take about a decade.
Because a) folks that are the most impacted by this cannot vote and b) IIRC there are even limits imposed on political activity by visa holders, they get slightly relaxed when you get a green card (but do check it out, IANAL and may be misremembering).