Seeking a little advice before I proceed with contacting local pros

Hi there! Hopefully this is the right place to ask this question.

Here's some context. My home was almost completely tiled in Saltillo dating back to the mid 90s. Unfortunately a massive plumbing accident caused much of the home to flood before we inherited it and we had to remove a majority of the Saltillo. Basically only the main bathrooms still has any of the 90s installed tile. I have been wanting to redo and update the bathroom that is mostly covered in it but I honestly don't want to go through removing it all from the combined floors and walls, nor do I really want to remove the last of the tile that my in-laws had lovingly chosen for this home. It's less about disliking the tile (which I don't, it feels kind of traditional and that's nice) and more about not really enjoying the current color tones.

I know staining is a possibility but I'm not trying to go darker or colorful, but rather a bit lighter. Is that something that can be done with Saltillo tile? If so what's the process, how time consuming, is it safe for a home that has a bunch of pets and kids, is that something all tilers can do or only specialists, etc? I know I could inquire with my local pros but I often feel like I'm wasting their time if I'm not requesting a quote or ready to hire for the work yet, which I'm not. So I figured this was my next best bet. I'm not looking for diy advice cause it's a process I don't want to try on my own, but instead just want to make sure I'm informed of what my options are before moving forward.

Thanks in advance for anybody who has insight.