When submitting a CV as part of my graduate school application, should I include hyperlinks?
The issues you point to are real and good to pay attention to, but links are too useful to simply not use them in situations like this. Here is how I approach this issue:

Definitely use links (unless there is an explicit prohibition or a guideline discouraging their use), where appropriate. They add a lot and can be very useful to showcase your work and projects (and general tech savvy and resourcefulness).

Don’t use the “click here for blabla” format for links in a PDF document. This would be confusing to someone reading the document on paper or on a PDF from which the link has been stripped. Instead the link text should be equal to the URL it links to (although it’s okay, and may be preferable, to strip the “https://“ header). Example: “see academia. stackexchange.com for blabla”.

In general, don’t assume that any reader can or will visit the link. The document must stand on its own and make sense even if the links end up being stripped out. So, consider the links as extras that can add useful context but don’t use them to communicate any critically important information.

Link text should be styled (color, underlining, monospace font etc) so it’s easily seen and understood as a link.

Don’t point to web pages with very long URLs that clutter up the page and will lead to visually jarring line breaks (which LaTeX’s hyperref package doesn’t handle well). If the URL is somewhat long but not too long, consider putting it in a footnote and shrinking the font size.

Don’t use URL shorteners to get around the issue of long URLs. They obfuscate the link destination and require the reader to visit the link to find out where it points to, which is an annoyance and a security issue.