What to do after a failed internal transfer?

My manager was not particularly happy about my transfer request, though he mentioned how the company is supportive of engineers seeking internal opportunities.

Sorry to hear this - Unfortunately most managers aren't supportive of reports leaving their team. This is why unless you're 95%+ confident that your manager has a mature mentality here, it's best to coordinate the entire move in secret (i.e. you let your manager know that you're leaving when the transfer is already finalized). It looks like this isn't feasible in your org/company.

What do I do to mitigate any potential consequences of the failed internal transfer (e.g. getting a poor performance review, being first on the chopping block for any layoffs, etc.)?

For performance review: Create a formal expectations plan with your manager and adhere to it rigorously. Check out our masterclass on navigating your performance review in tech to learn how to that.

For layoffs: The only thing you can really control is your performance here, and front-line managers generally don't have a lot of say in who gets laid off. Check out this in-depth discussion on how layoffs work and what you can do about them.

Given the frayed relationship with your manager, your relationship with others on the team becomes more important. If you have glowing relationships and peer reviews from others, your manager won't be able to justify a poor rating for you.

However, given that your manager wasn't happy, I would not expect them to advocate for you. So things like promotion will unfortunately be harder.

Which level are you at? My answer also depends on your seniority a bit (senior+ might be easier to build more relationships outside the team)

Thank you both for your feedback! I'm reviewing resources regarding layoffs and performance reviews, and they're quite helpful.

I'm an entry-level engineer. I'm able to foster my relationships with my teammates, though it'd be harder to foster any on other teams in my current scope.