Is there a reasonably simple way to automatically generate unique tags for definitions, propositions, lemmas, etc.?

Perhaps something like this. (This example uses LuaLaTeX, but the basic approach works the same in any engine.)

documentclass{article}
usepackage{newcomputermodern}
usepackage{amsthm}
usepackage{microtype}
usepackage[bookmarks,
            colorlinks,
            destlabel,
            unicode]{hyperref}

% You would set the PDF title, author, etc. with package options or
% hypersetup.

setmathfont{XITS Math}[
  range = QED,
  Scale = MatchUppercase ]

renewcommandqedsymbol{ensuremath{QED}}

theoremstyle{remark}
newtheorem*{joketheorem}{Russell’s Remark}

title{A Remark By Russell on Vacuous Truths}
date{13 March 2021}

begin{document}
maketitle

begin{abstract}
This paper recounts a clever extemporaneous hyperref[rem:vacuous]{illustration}
by Bertrand Russell of the concept of vacuous truth.
end{abstract}

clearpage

Once, when Bertrand Russell said in a lecture that any proposition whatsoever
follows logically from a false premise, a student asked him, ``If (1 + 1 = 1),
does that prove I'm the Pope?"  Russell replied:

phantomsection % Add an automatically-named link target.
begin{joketheorem}
label{rem:vacuous}
If (1 + 1 = 1), I am the pope.

begin{proof}
I am  one.

The Pope is one.

One and one are one.

Therefore, I and the Pope are one.
end{proof}
end{joketheorem}

end{document}

The abstract links to the theorem in the body of the document, with the relative URL #rem:vacuous. A ref or autoref would also work for a numbered theorem. You can give out an URL like https://some.edu/~someone/papers/russell.pdf#rem:vacuous as well. The destlabel option causes each link destination to be named automatically after the following label.

If you want a perma-link to an official version of the document, you can set the baseurl as a package option or with hypersetup.