When did other slavic nations adopt the Latin-inspired look of printed Cyrillic pioneered in Russia?

Question

Russian Emperor Peter I famously reformed the Cyrillic script in Russia, where, among other changes, he redesigned the letterforms to more closely resemble the look of the modern Latin script.

Here is what printed Cyrillic (set in the Poluustav script) looked like in Russia in 1703, before the reform:

And here is the first book printed using Peter I’s Civil Script, in 1708:

(See Civil Type and Kis Cyrillic for a comprehensive analysis and history of the reform.)

Naturally, this is the style of Cyrillic that has defined the script’s modern day look: вот пример современной кириллицы для печати русского языка. Though the traditional, blackletter-esque script remains in use today, it’s reserved for liturgical texts and is considered antiquated.

Now, my question is: when did Slavic nations outside of the Russian Empire (e.g. Serbia, Bulgaria, etc.) adopt this new Latin-inspired look? Are there historical records documenting their transition, like the comprehensive accounts of Peter the Great’s controversial innovation in Russia?

The Poluustav letterforms could be found in pre-1700’s printed books for many varieties of Cyrillic. In fact this style of manuscript writing had been allegedly invented in the Balkan region before it found its way to what later became Russia. However, the only Cyrillic style that’s in use nowadays, across all nations that use Cyrillic, is the Civil Script-based reformed variant.

Answer 1

That reform was not only about scripts or fonts. See old\church Slavonic Cyrillic and how it evolved into civil modern Cyrillic fonts and why Азбука (Alphabet) was reduced also.

Though I understand some would wish so, I also doubt it was Latin inspired. Enough to have a look at XVII-XVIII (and even XIX!) French, British, German books. Not every modern French, British, German could easily read them.

poluustav … in its struc­ture it was a form of me­di­ev­al hand­writ­ing

No. It was just an old Slavonic alphabet. As for «me­di­ev­al hand­writ­ing» — it was very variable — I bet you put into one entity here

1. «free civil fast hand writing» (i.e. Скоропись — I don't know English word for this)
2. «civil hand writing» (i.e. Пропись which is cursive in English or «hand writing»)
3. «books hand writing» (you call it a form of «me­di­ev­al hand­writ­ing»)
4. «books printed types» (the example of which you call «poluustav», ther were a lot of types of it, like https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D1%83%D1%81%D1%82%D0%B0%D0%B2_(%D1%88%D1%80%D0%B8%D1%84%D1%82)#/media/%D0%A4%D0%B0%D0%B9%D0%BB:LavrentyevskayaLetopis.jpg there was also ustav = устав)

Peter’s first at­tempt to lat­in­ise the Cyril­lic al­pha­bet. ... The lower­case let­ters of the Dutch typefaces were re­lated to both the civil hand and poluustav.

No. Just to old Slavonic alphabet, where some letters were the same as in a modernized (by Peter's reforms) Slavonic alphabet.

This was prob­ably the reas­on why Peter fi­nally took a dis­like to Dutch print­ing and made the de­cision to move the design of the new type to Rus­sia.

Thus, no. It was not a new type. It was also a reduced alphabet and thus a reformed grammar.