昨日より、強めに怒られたのだろう
In this sentence specificly, Apparently it means "was scolded more strongly than yesterday" based on the context but does it mean that you can use a ます stem of a verb + に to make it an adverb? Or is it related to the ます stem + に + 行く (to go for the purpose of doing something) but with just a different verb?
In general, you can not join ます + に, but you can join na-adjective/noun + に.
You are confused because you are thinking of 強め as a verb, but it is not. The verb is 強める, not 強め. 強め is the 連用形 (or ます stem) of the verb. Take a look at the second entry for 強め at this weblio page (emphasis mine):
マ行下一段活用の動詞「強める」の連用形、あるいは連用形が名詞化したもの。Conjunctive form of an ichidan verb in the マ column, or alternatively, nominalization of the conjunctive form.
While it's true that 強める is a verb, what you are seeing in the sentence under discussion is a nominalization of the 連用形 (or ます stem) of this verb, i.e. 強め is being treated as a noun. Consequently, you can add に to it just as you would do with any noun and turn it into an adverb.
Note that this is not to say that any 連用形 form (or ます stem) of a verb can deliberately be nominalized, but other nominalizations come to my mind such as 出来上がり (from 出来上がる).
Or is it related to the ます stem + に + 行く (to go for the purpose of doing something) but with just a different verb?
It is not related to the grammar (ます stem) + に + 行く.
