Yes, I think you are heading in the right direction with editing the CSL file to get the package version number to show in your bibliography. In the bibtex entry the pkg version number is in the 'note' field, which most citation styles do not include when generating the bibliography.
Here's how I edited the-company-of-biologists.csl file to make the note field show in the bibliography. I opened the file in a text editor, then among the lines that define macros, say around line 57, I added this:
<macro name="note">
<text variable="note"/>
</macro>
then further down where I saw the item title being set, I added this line:
<text macro="note" />
in this group of lines, to show the context of where exactly I added that:
<group delimiter=" " prefix=" ">
<text macro="title" font-style="italic" suffix="."/>
<text macro="note" />
<text macro="edition"/>
<text macro="editor"/>
<text macro="publisher"/>
</group>
And when I knit my Rmd with this modified CSL, I get this in the reference list:
Borchers, H. W. (2021). Pracma: Practical numerical math functions. R package version 2.3.3.
Is that what you are after? Of course it will print the note field for all items in the bibliography, so some editing of the bib file might be required to remove unwanted note text in journal articles etc. Perhaps there is some logic that can be added to the csl file so that notes are only printed for Manual type items? In any case, let me know how that works for you!