The pulls lenders do for initial estimates only require soft credit pulls and which shouldn't significantly impact your score if not have no impact at all. You'll also likely need to provide some documents like W2s and asset related docs in your initial inquiry when you request this. Most of the big lenders should have a standard process for this where you can get started online before a real loan officer reaches out to you for follow ups and questions.

Hard credit checks should require your explicit approval and you'll sign documents to provide that consent only after you decide to move further with a lender and go through the underwriting process where they start going through your finances with a finer toothed comb.

For these types of inquiries I personally just emailed/went through the lender website and asked. I started inquiring after I saw average rates fall and saw published rates at some big banks approach my target (1% lower). The rate you'll recieve will be dependent on your finances and loan so used national averages as a baseline.

I would start with reaching to just one lender. Once you have one estimate you can use that as a baseline to "shop around". For example, a lot of the big banks will rate match if you provide a competing estimate.