if this is the experience in a team, then the team already has a problem. i expect these things to be made clear up front.
when someone joins a team they should be assigned a mentor whom they can ask any question, no matter how dumb, and the mentor then guides the new team member in how to approach such a question, which at that point can include asking the LLM. it is the mentors responsibility to point out when it is ok to ask another senior developer. daily standups can also help with this sort of thing.
in a close knit team i would also expect that either everyone can ask anything from everyone else, and that everyone learns when it is ok to ask questions. the situation you describe should simply never arise. if it does, then something is going wrong
Alternative take: the assumption that senior engineers get pressured into agreeing to mentor without it formally being an acknowledged part of their job - that is, that a significant percentage of their time is supposed to be allocated to making themselves available to juniors - is fundamentally a problem.
There is so much stigma associated with being an senior engineer that simply wants to spend 95% of their day working on the problems that they were hired to solve. The worst part is that the vast majority of people in this situation are not compensated for this time, and they are expected to keep up with their actual assigned responsibilities.
This state of affairs is a relatively new thing. The idea that you would join a company with the expectation that the most important people to the success of a project should drop what they are doing to context shift to someone else's problem several dozen times a day is not something that would have been remotely normal twenty years ago.
I am not saying that mentoring is bad or that asking for help is bad, just that there's been a change and the unspoken vibe is that if you're not happy to work at ~30% capacity because you need to mentor people, you're some kind of antisocial jerk.
If a company wants seniors to mentor, pay them to mentor. It's very simple.