Learn English – Which is correct, “be embodied in” or “be embodied within”

Yes.

It’s very tempting to leave the answer at that, but… some more notes.

1. The most cursory look at any newspaper, or around the blogosphere, confirms this answer. ‘Last week’ is common as muck, while ‘yester-week’ is virtually non-existent, and when it does appear, it’s for archaic effect.

2. ‘Last week’ isn’t in any way incorrect. It’s had the meaning ‘most recent, latest’ for over 600 years: in 1411, for instance, the rolls of Parliament under Henry IV refer to “The last parlement…” (OED.)

3. As your sources point out, however, ‘last’ can sometimes be ambiguous, and ‘latest’ is often a good alternative in those cases. Talking about ‘the latest week’ sounds odd and affected, just as it did when Fowler wrote; but talking about ‘Madonna’s latest single’ is perfectly fine.

4. ‘Yester-’ isn’t actually as archaic as we tend to think! A few examples — ‘yesterday’, ‘yesternight’, ‘yester-eve’ — are old, but (according to the OED again) the general combining form (in eg ‘yester-week’) only really shows up in the 19th century. Amazingly, even good old ‘yester-year’ was apparently only coined in 1870, by Rosetti translating Villon: “Where are the snows of yester-year?”

5. Finally, none of the sources you give support your implication that ‘yester-week’ is the correct usage that should be preferred to ‘last week’! The Bierce and Fowler quotes point out the illogic and occasional ambiguity of ‘last’ (note that neither of these makes it grammatically wrong); Fowler’s suggests ‘latest’ as a sometimes better alternative, but neither even mentions ‘yester-’! The OED simply points out that ‘yester-’ exists (at least, existed for a few decades) and means roughly the same thing.

Not sure if you were asking only about your example, or more generally, so I’ll answer more generally. Consider these uses:

1. He hung his coat in the closet.
2. He walked in the door.
3. I’ll have it finished within an hour.
4. It is almost within his grasp.

Consider swapping the words (within/in) in each of the four cases.

1. This sounds silly, to my ear.
2. This would make no sense, unless the door is hollow, and the person is very small.
3. The meaning here is close, however, I’d suggest that “within” implies that I might have it done before the hour is up, but “in an hour” implies that it will take every bit of 60 minutes.
4. This is also close, but “within” carries a greater connotation of the distinction between “in and “out”.

Latin uses different cases for each of these (ablative of time within which, for number 3, which is relevant to your example.

I was glad to see the question, because I see “within” used excessively in my technical field, as in, “the information resides within the database” and other pomposities. This is written in "formal" documents by people who would never say, "I hung my coat within the closet", but who think it sounds scientific, or erudite, or something when written in a technical paper.