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I encounter such a sentence in a homework assignment:

It seems that the burn-in is adequate, that they are all converging to
the same-ish posteriour value, and that there is good mixing.

I don't know if the -ish is appended here just to reduce the extent of sameness? Is it just a synonym of similar or alike and etc?

And can I add -ish to any adjective to convey a same-ish meaning?

Adding an '-ish' at the end of a word is generally done in informal contexts, mostly to make the reference sound deliberately vague and approximate. (Source)

Here, the speaker has added the suffix because he isn't completely sure of the similarity with the posterior value.

You can add the suffix to words, to bring about a hint of uncertainty. For example,

Person 1 : What time is it?
Person 2 : I don't know. I think it should be around twelve-ish?

Update

As pointed out by Michael Kay, if the adjective points to an extreme, then '-ish' implies less extreme; 'small-ish' is less small than small; 'cold-ish' is less cold than cold; 'same-ish' is less similar than same. So '-ish' not only conveys approximation but can also assign less of the characteristic than if "-ish" were omitted.

Another answer already explains the meaning of -ish, but I'd like to address this question you also asked:

can I add -ish to any adjective to convey a same-ish meaning?

My answer to that would be: perhaps – but don't overdo it.

The suffix works well for some adjectives, such as colors:

They're so slow that sedentary that algae grows on their coats, giving sloths a greenish tint that can be used as camouflage in the trees. (Indianapolis Star, 2018)

However, I would NOT recommend applying the suffix haphazardly to just about any adjective. There are many cases where an -ish suffix would sound, well, amateurish, where it would probably be better to avoid using it, especially in formal contexts.

For example, consider size adjectives. Adjectives that connote extremes (such as tiny, infinitesimal, massive, or vast) don't work very well with -ish, and the ngrams reflect that.

Also, if a friend asked if I was hungry, I suppose I could say, "I'm hungryish," but most natives would opt for a phrase like, "I'm kind of hungry," or "I'm a little hungry," instead, and the ngrams support that, too.

Other adjectives that sound odd with -ish would include: delicious, tired, or miserable, but faint and loud seem to work okay:

Two-thirds the way along the Arcturus-to-Vega line brings you to a pattern of four faintish stars resembling the shape of the stone block (The Telegraph, 2017)

On Monday night, a few dozen noodleists came out for cocktails, soup, loudish Ramones and the bar's retro, antique-radio vibe. (New York Times, 2014).

If your spellchecker puts a red squiggly line under a word with -ish, it might be better to use an adverb like rather instead. (For example: He was rather thirsty after the game might be a safer option than He was thirstyish after the game.)