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This press release by an Italian union mentions a huge difference between the number of academic positions in various countries:

Per fare solo un esempio, sul personale, a fronte dei circa 50.000 docenti universitari nel nostro Paese, ce ne sono circa 250.000 in Germania, 200.000 nel Regno Unito, 95.000 in Spagna, 80.000 in Francia e analoghe differenze si verificano rispetto al personale tecnico e amministrativo.

My translation:

As an example, let's mention personnel: corresponding to about 50,000 university professors in our country [Italy], there are about 250,000 in Germany, 200,000 in the United Kingdom, 95,000 in Spain, 80,000 in France, and there are similar differences regarding clerks and technicians.

Are these numbers accurate? Do they compare apples to apples? For instance, as far as I understand, many PhD students in Germany are employed as "Wimi"s and would probably be counted as "academic personnel", while in Italy they are still considered students and they would not fit in the same category.

Regarding Italy, this 2018 press release by the Italian ministry of education shows that in 2017 there were 54,235 academic positions in Italy, counting only professors and junior positions, both temporary and tenure-track (Professore ordinario, professore associato, ricercatore a tempo indeterminato, ricercatore a tempo determinato). This excludes postdoc grants (13,946) and all PhD students (9,288 in 2017 according to another source).

Where can I find similar breakdowns regarding Germany, UK, or other countries?

The data is roughly accurate for France. The French ministry's HR department releases data periodically, and one of the latest report (2017-2018) is available there: http://cache.media.enseignementsup-recherche.gouv.fr/file/statistiques/62/3/Note_NP_2017_2018_1146623.pdf

In summary, in 2018, there were 81,563 teachers in French public universities. This includes 62,491 permanent positions (full professors, lecturers, and full-time tenured teachers), and 19,072 non-permanent. Of these, 7110 are PhD students with teaching duties, and 4500 are "ATER" (a kind of "postdoc", it's complicated). Depending on how you want to count what, the 80k figure is probably overestimated if you exclude PhD students and postdocs, but it's in the ballpark.

The numbers for Germany are definitely counting different things. Take the following official source

https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Bildung-Forschung-Kultur/Hochschulen/Publikationen/Downloads-Hochschulen/personal-vorbericht-5213402188004.html

On page 98 is the full list, in which a number around 250.000 indeed occurs, but as the number of total full time scientific personal, which on one hand includes 193.000 "Wissenschaftliche Mitarbeiter", i.e. PhD students and Postdocs, many of which will be involved in teaching, but only some of which might be counted in similar statistics for other countries. So if you count only full professors and "Lehrbeauftragte", you will actually get a lower number then for the other countries, but then again you will have missed many non-tenured people you would have counted in other countries.

Also this number excludes around 100k part-time (which can mean anything from giving a small one week-course once a year up to 49% of a position) "Lehrbeauftragte", which often do the similar work to professors especially at "Fachhochschulen", where most of them teach.

I think it is impossible to get comparable numbers for a common definition of "university teacher" for the different countries. Personally I would go the other way and compare the number of full time scientific (teaching and academic research, especially including paid PhD Students) personell between the different countries instead.