Your reaction to "trainings" may have been, "But that's not a countable noun; you can't make it a plural".
This subject came up recently in an online discussion among editors, and there was a lot of hostility toward "trainings". The usual sorts of comments about shuddering and teeth grinding and laments about how common it is, and should be replaced by "training sessions".
Someone felt that "teaching" was also not used in the plural, and expressed gratitude for this oasis of "sanity". This despite the fact that we have evidence of "teachings" from 500 years ago:
1542–3 Act 34 & 35 Hen. VIII c. 1 Suche bookes, writinges..teachinges and instructions, as be pestiferous, and noysome.and no-one would bat an eye at a phrase like "the teachings of Buddha".
By the way, I hate it when people use "sanity" to describe their particular usage, with the implication that any new development in language (by someone else) is "insanity".
But the most intriguing comment implied that this irksome use of gerunds as countable nouns is something new. See the (partial) list above of very common plural gerunds.
Now, it's true that "trainings" is not as well-established as some of the gerunds I've listed above, but it has become quite common in certain fields since the 1980s, and there is no reason to object to it. In fact, I wouldn't be surprised if 50 years from now some editors were to comment, "Training sessions? That's so redundant! Why say that when you can just say trainings?"
What's more, this is one of these "way older than you think" usages.
1598 I. D. tr. L. Le Roy Aristotles Politiques viii. iii. 384 It appeareth, that..it is needfull to learne certaine things, and to be instructed and trained in the same, and that these instructions and trainings be vndertaken for their sakes which learn.
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