For myself, if I have the left panel minimized, when I open any project it's minimized. If it's open, then when I open any workspace the panel is open... I think this is a setting per user, not something that you can save for anyone else. I think this would be something that each user would have to minimize themselves....
As @MandyGeorge said, I think the "Share Workspace with Anyone" feature, being specifically a view only interface shouldn't contain the left components panel, but that view comes with its own set of challenges.....
The problem with the "View Only" permission is that it also kills the ability to change the date range... so in my org, I have to give everyone Duplicate permissions just to allow them that access which is required.
I wish there was something in between... I don't really like the Share with Anyone myself, and have no used it at all. I hate to say it, but Google's Looker Studio having a View vs Edit experience would be an ideal solution... even for myself. If I just need to open a report to check some numbers I don't need the whole editing interface (there would still be an option to switch between View and Edit mode of course, so if we have to do any ad hoc breakdowns or dig a little deeper into the data we have it readily available)