Looking at the size of the potential PhD advisor's lab: e.g., if many (>10) PhD students or post-doc, then likely to be quite hands-off.
Asking current or former members of the potential PhD advisor's lab. (but sometimes it is difficult to establish contact with them and obtain a frank answer, plus that's a bit tedious to do for each potential PhD advisor's lab).
Directly asking the potential PhD advisor but I am unsure whether this is a wise approach as for example if the prospective PhD student is asking the potential PhD advisor whether they are hands-on or hands-off, this could be construed as being too much dependent or independent from the PhD advisor (e.g., a hands-off PhD advisor would typically prefer independent PhD students), which might reduce the chance of being accepted in the PhD program in case of mismatch between the PhD advisor and prospective PhD student.
What could be other techniques for a prospective PhD student assess whether a potential PhD advisor is hands-on or hands-off, preferably without impacting that chance is to be accepted in the PhD program?
I would suggest looking at the PhD thesis of former students of the advisor, especially at the thank you/ acknowledgement part. All of them will thank their advisor (no information there) and most of them will thank their parents (also not useful for you) but usually there will be a whole paragraph or two about the advsior where the students explain why their advisor is awesome. This will contain a lot phrases that let you judge what kind of advisor they are.
I agree with your methods. I know other techniques:
Check the publication list of the advisor. More than 20 publications per year as last author means that the advisor prioritizes quantity over quality and has no time to be hands-on.
Check the website Labvisor to see if there are any reviews from your potential lab.
Take a look at the advisor's office. If it's a mess it means the advisor has no time to organize it nor to be hands-on.
Ask the potential advisor how is the process to write/author papers. If the advisor just does the final review, that indicates a hands-off approach.
Is the advisor on the board of the Faculty or any other research institute? If so, the advisor has no time to be hands-on.
Check the websites PubPeer and Retraction Watch and see if there are comments on the advisor's papers. Draw your own conclusions.
Is the advisor wearing a lab coat? Then they are hands-on. If they wear a business dress, they might be too busy in meetings. Ask if there is a dress code in the office.
Ask something related to travelling. Is it normal to travel to research partners locations OFTEN as a PhD? To where in the World? Are there many potential conferences to travel to after the pandemic? A lot of travelling means hands-off.
Ask if you should collaborate with their current PhD students or just with the advisor. In the former case, they may be hands-off.
Is your potential advisor a PI? Being PI involve a lot of responsibilities that give no time to be hands-on.
Edit: These might be heuristic "techniques", like indirect questions in a job interview, that can give you a sense of how the potential advisor works. Of course one can not draw 100% certain conclusions from them. But some of these insights might be confirmed by some PhD candidates' experiences. What do you think?