How can I protect time for high-priority work when my manager keeps assigning low-impact tasks and undermining boundaries?

You need to communicate clearly about priorities every time you are given a task.

So when you are given a "low-impact internal task" you should not assume that he "seemed to expect immediate turnaround". Ask explicitly whether this is more important than the time-sensitive, high-impact client deliverable. Explain that it will take N days and will delay the client deliverable by N days plus a few, for context switching. Is he OK with this? Then send him a brief email summarising what you said and his decision.

Regarding "pulled into a discussion": first if your boss thinks you are vital to communication, that puts you in a great position regarding your value to the company. Don't be upset about it. And try to not to second-guess your boss about whether someone was blocked. If you've asked explicitly about the priorities, and given your boss the information, it's up to him to direct your time.

One possibility is that your boss doesn't have a stake in "time-sensitive, high-impact client deliverable". He may not be directly responsible for its delivery. If that's the case reach out to someone who does have a stake, and communicate that your contribution is being delayed by other tasks. Ask about the status of the project - it may not make any difference to the total project if your part is delayed a bit.

In the end, if you've communicated the situation clearly, and asked about priorities, it is up to your boss to set your priorities. That's what he's paid for.

I guess that you are past the risk of being seen uncooperative, since you are actually being such.

I recently had a conversation with my manager where I set a boundary

Nowadays, everyone sets boundaries. Of course it's great to set them in personal relationships, but here we are in a workplace and your "boundary" is totally meaningless: it's up to your manager to, duh, manage your time. I see as arrogant from your side to decide unilaterally on what you can or can't work.

we both agreed it should take priority.

Allow me to define better what "priority" means for a manager. It means that you are supposed to work most of your time on that specific task. This does not necessarily imply that you are not going to work on anything else. It's perfectly possible to have your main, priority, activity on which you spend, say, 80% of the time, while you are also taking care of other tasks on the remaining 20%. And it's possible that some of the non priority tasks are actually closed earlier (it's pretty common indeed, since often those tasks are smaller).

Shortly afterward, my manager did two things that felt like a direct violation of that boundary:

No, there isn't any boundary here worth to be enforced. He is just doing his job in deciding who to involve from his team to solve problems. He might be wrong of course.

He assigned a low-impact internal task (not time-sensitive, with limited value), and seemed to expect immediate turnaround — even though I was in the middle of the urgent deliverable.

Let the manager decide what is urgent and what is low priority. It's apparent the you are not aligned on that, but that's his decision, not yours. And if you want to be seen as cooperative, ask explicitly about expectations on turnaround. Discuss if the priorities should be revised. Not going further on this point, since other answers already covered it.

He pulled me into a non-urgent internal discussion that could have happened asynchronously or without my involvement. When I responded reiterating that I don't want to be pulled into said discussion, he escalated and claimed others were “blocked” — although, from what I can tell, no meaningful delays occurred.

Again, how it should have happened it's not your decision, you can give an input. And your reaction is basically the strict definition of uncooperative. You didn't care that other people couldn't do their job and use this curious term, "escalate", when he apparently didn't involve anyone else. Rather, he mentioned two valid reasons: people are blocked and you facilitate the communication (which is a great compliment to take home, btw). He might be wrong, but he nonetheless offered a rationale behind his legit decision.

If he pushes back, I’ve debated whether to loop in the business stakeholder to realign on what matters most — but I also want to avoid unnecessary escalation or being perceived as difficult.

Ok, he "escalated" by simply stating his reasons, now you want to go nuclear just because the boundary thing. And he is the manager, there is nothing he can really "push back", it's just you that are pushing back tasks based on your view. However, don't worry about the last sentence, as I see extremely unlikely that you are not already perceived as difficult and uncooperative.

How can I maintain boundaries to protect my deep work time without escalating conflict or being seen as uncooperative?

You don't set boundaries that are not up to you to set in the first place. You can try to convince the manager that it's better if you work 100% on that task, but, ultimately, it's his decision and no boundary from you can limit him from doing his job. Of course, you can leave if you don't like your manager, but, if your goal is really to cooperate, you better leave aside the "I'm entitled to work only on what I want" attitude.

Key thing - "Manager".

All you can do is politely document by reminding them them that you've already been assigned a higher priority task. If they don't email or text back, then you do confirming email/text that you will be right there as the asked.

Assuming the Manager is just overwhelmed, they might (maybe) appreciate being reminded about the priority. If they don't get them importance of priorities and how to manage, then you have CYA. But they are the manager.

You may have the domain knowledge, but they are the one that gets to play havoc with the priorities. If you take it outside of the one-to-one relationship then you've missed the point of:

• Do it
• Ask for clarification
• Suggest a better plan

It's good that you're setting boundaries. When this happens, you can remind your manager that no matter what, you're leaving the building at your regular time out of the door. You can also start creating a paper trail to CYA - a quick "memorandum of understanding":

Dear boss:

On XX/XX/XX date, we discussed the urgency of completing project XYZ on time by YY/YY/YY, and you acknowledged my need for uninterrupted time in order to do so. However, today you insisted on me spending XXX hours of time on project ABC instead. It'd be great if we could be more mindful of any consequences of missing our deadline. Please be aware that I'm not in a place where I can sacrifice personal time to make up for any lapse.

You might re-word it according to your tastes, but definitely hold your manager accountable for the conflicting priorities.