@Neith posted an excellent thought-provoking answer; after I read it, I contemplated the factors he listed and then found myself thinking whether we are not overlooking the elephant in a room. So I decided to post my humble thoughts as an answer in order to complement what @Neith said.
I guess that most Tsarist era writers were highly educated people belonging to the upper classes of the society. They had very good manners, and using rude expressions like "чёрт побери" was very unnatural to them and perhaps even shameful. After the revolution they fled from Russia en masse and were replaced by new writers, who had belonged to the lower classes of the society and essentially were ill-mannered peasants and workers. Phrases like "чёрт побери" were their natural expressions, and they saw nothing bad or shameful in using them. And the communists gave them the opportunity to publish books.
Thus, I humbly think that an important factor may be simply the replacement of the writers. Тhe observed rise of use of "черт" may simply reflect the manners of the new authors. As simple as that. And this is the elephant we may be overlooking.
The Tsarist censorship did not ban the word "черт," as evidenced by numerous examples of the use of that word in books of the Tsarist era. I especially like this one:
ЧОРТ И СМЕРТЬ
— Куда, курносая? — Иду я за душою;
— Къ кому? — Къ Секретарю, такъ велѣно Судьбою!
— Ахъ! какъ проста Судьба: живетъ она въ глуши.
Какой въ Секретарѣ, какой искатъ души!
Но еслибъ и была, то вѣрь, что прежде смерти,
Ту душу за алтынъ купить успѣютъ черти.
(From a book of 1841)
This is a wonderful piece of Russian poetry, and I really like it. It is a very elegant way to express quite an artistic thought. That's a style of a well-educated, highly intellectual Tsarist era writer.
And now compare that style with the following piece of poetry of the Communist era:
Их голод не душит, и юнговский план
Не знает дороги в их толстый карман.
Запомни: тоскуют по ним фонари -
Они ведь свободны, чорт побери!
(From a book of 1931)
The expression "чорт побери" was used multiple times in that poem. What I quoted above is just a small excerpt. I think it is a nice illustration of my point about manners of Communist era writers.
Thus, I suspect that the rise of use of "черт" may be simply a reflection of manners of new authors who came as a replacement of Tsarist era writers.
As a general remark, I subjectively find the Tsarist era literature richer, more artistic, and better mannered than the Communist era literature. Most prominent Russian writers were Tsarist era writers. The October Revolution appears to have had a considerable effect on the Russian literature.