How to manage the underscore in DOI or url specifically in BibDesk?

What is the recommended method?

We cannot replace "_" by "\_" because in the DOI or url field of BibDesk, there 
is a little icon which open the browser to the DOI website with the number in 
the DOI field, or to the url displayed in the url field, and an address like 
https://www.my-example.com/a\_test is NOT the same address as the address 
https://www.my-example.com/a_test.

AND if the "_" is not replaced by "\_", the preview TeX for the bibliography 
entry cannot be created (a red error is displayed instead).

So, please, what is the recommendation for this problem? A complete guide to 
this problem can be useful (on the website or the user help).

If the file ~/Library/Application Support/BibDesk/previewtemplate.tex has to be 
edited for this problem, what is the edit to do? I have tried adding 
\usepackage[strings]{underscore} in the preamble, but this don't work 
(suggested here: https://tex.stackexchange.com/a/523253/132405).

I don't understand why the DOI organization has chosen the character "_" as 
available character for DOI numbers, as the TeX world uses a lot of DOI, and 
"_" is special in the TeX world, but this is another question, not for here.

For testing, I use in the setting, TeX preview, the "elsarticle-num" BiBTeX 
style (manually entered).

By the way, why this above popup menu don't display all available .bst in the 
LaTeX installation, a least the .bst in 
/usr/local/texlive/2024/texmf-dist/bibtex/bst? If this list is too big, there 
is perhaps a middle between the actual situation (it displays only abbrv, 
abbrvnat, acm, alpha, amsalpha, amsplain, apalike, gerabbrv, geralpha, 
gerapali, gerplain, ieeetr, jurabib, jureco, plabbrv, plalpha, plplain, 
plainnat, siam. Not abbrv-fr, plain-fr for the French, for example).

The help says about the list in the popup menu: "This is a list of generic 
styles that may or may not exist on your system." Perhaps, but why few styles 
for German or Polish, and not French (and other languages)?

Thanks.

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