They didn't need to search, they just needed to wait outside to arrest. That would have worked if the defendant didn't use the backdoor.

But they didn't have a valid warrant for arrest. Therefore him going out the back door was not "escaping arrest".

They did have a valid warrant for arrest, they just didn't have a warrant to search the courtroom but they had a warrant to arrest the guy as soon as he stepped outside.

Then they weren't obstructed. They're just shit at their job.

If I know you're in a building and haver permission to arrest you, it's not "obstructing arrest" if you use the back door. What if your car's parked out back?

To quote the 10 year old who destroyed me in fortnite "Get good."

I could be if you can't enter a store to arrest someone and back door is marked "private employee only". Manager then let's them out the back door despite clear enforced store policy to prohibit random customers from being allowed in that part of the store.

I don't think the manager (or any other employee) is legally obligated to follow store policy in your example.

FBI should review thier fieldwork, alternate entrance/exits, must be secured or under watch, before the approach.

They did catch the guy so they did do their job.

yeah they did thier job, but operationally speaking, they need a review.