David's excellent answer has reminded me, there is a very comprehensive work by C.D. Ginsberg.
Ginsberg's work, written in 1896, predates the BH/BHK/BHS and covers the first and second rabbinic bibles by bomberg, which are from the 1500s. It describes some hebrew masoretic manuscripts that have and some that don't have, those two verses. Though which ones the BHS used is another matter.. But perhaps the closest we can get is this.
David provided a comment with a screenshot included here, showing that the BHS in its explanation of Ms(s), mentions Kennicott, and De Rossi and Ginsberg, and perhaps others.
Furthermore, here is a screenshot from BHS 5th edition, we see that Ms(s) includes more than those three(eg the Cairo Geniza is mentioned), and that Ed(d) also mentions those three.
BHS introductory pages also mention that mlt=multi, exstat=it exists.
So therefore since BHS mentions those works, it makes sense to look at those works. kennicott, de rossi, and ginsberg.
As you see from the screenshot, BHS also mentions fragments from the cairo geniza, (there has been a project to digitize the cairod geniza https://cudl.lib.cam.ac.uk/collections/genizah/1 )
David's answer looks at De Rossi's work. I'll look here at Ginsberg.
According to https://stepweb.atlassian.net/wiki/spaces/SUG/pages/24215583/More+about+OT+Editions Ginsberg's work only looks at "manuscripts from the thirteenth century onwards that were in the British Library".
C.D. Ginsberg's work is available here https://archive.org/details/MassorahMassorethMassoretic in what look like many PDFs but a comment gives a link here to what looks like it in two PDFs
The PDFs aren't that big either. vol1 is 28MB, vol2 is 43MB
Volume 1 is at
Volume 2 is at
A helpful table of contents in the pdf mentions
and the title of Chapter 12, (which is where vol 2 begins)
and that there is an index of manuscripts
On Page 1003-1005 He has a table of manuscripts all (perhaps most, but probably all), are hebrew manuscripts.
Vol 2 begins with chapter 12 which has a title which is exactly what i'm looking for
On Page 494-495
I'll look through some more, there may be other manuscripts, but for any of them, though it's worth bearing in mind that Ginsberg work is regarding masoretic manuscripts used by the 1525 Bomberg "rabbinic" bible, rather than by the BHS. (The BHS is based largely on the leningrad codex, though clearly a deviation from that is those two verses Joshua 21:36-37, even there the BHS has them in small print probably because they're not from the leningrad codex). So this would state hebrew manuscripts that has them, rather than the particular ones used by BHK/BHS). Also Ginsberg's work on the 1525 bomberg "rabbinic" bible, was published in 1896, that happens to also be before the BH/BHK was published - the BHS/BHK and of course BHS, was published post 1900-
He mentions on p178-180 and p434 some reasons why the 1525 bomberg rabbinic bible excluded them, though e.g. the 1521 bomberg bible included them. And he is of a sure view that they should have remained included. He indicates that they're in many if not most of the earliest manuscripts. (while he doesn't mention the following, they're clearly not in the st petersberg(i.e. leningrad), or the aleppo. He mentions the verses briefly on p434
Looking further, It seems to me that he doesn't discuss in detail, all the manuscripts that he mentions in that index, but he discusses 24 of them in some detail, as seen in the vol 2 pdf. I don't think he had access to the Aleppo Codex (I doubt Bomberg did either)..
He discusses the St Petersberg Codex (that became known as the Leningrad Codex when the city Petersberg got renamed Leningrad in 1924.. But at the time Ginsberg was writing it was known as the St Petersberg Codex). Though he doesn't mention those verses in connection with that codex(though we know, as shown from the question, that those verses aren't in that codex). But he does describe other codexes too and with those, he sometimes makes mention of whether they do or do not have those two verses.
In the red box I drew in, is a list of all references to those two verses. It seems to me that the earlier page numbers he's describing why they weren't in the 1525 bomberg but should've been.. And anything between p469-778 is discussion of 24 manuscripts, some of which he says whether or not they have reference to those two verses, and after p778 are just further mentions of those two verses.