I've looked at this question: Differences between “muss gut gewesen sein” vs. “musste gut sein” but I'm still not 100% sure what the difference is between:
Das wird bis Freitag fertig gewesen sein. (This will have been ready by Friday ???)
and
Das wird bis Freitag fertig sein. (That will be ready by Friday)
The first sentence sounds weird to me!
While both sentences (and your translations into English) are correct, so is your feeling of the first(corrected after comment) sounding weird.
Whether you are a native German speaker or, most probably, learning German from the background of an native English speaker, the first example example
Das wird bis Freitag fertig gewesen sein.
is highly uncommon in colloquial and spoken German, and quite rare in written context, which explains your feeling of weirdness about it. A lot of native speakers won't even be able to identify the tense correctly, especially if used in combination with Konjunktiv or subordinate clauses.
What we are looking at is the following construction:
This tense is called Futur II. It expresses an estimation, that an action has been completed at some future time, which in my opinion and contrary to the opinion of @Janka gives enough reason to call it Futur II. From my experience, native German speakers tend to underuse some tenses while also using others wrongly. This causes quite a dilution. For example, in spoken German the Präteritum is very rare, as it is mostly replaced by use of Perfekt. Most often, a future-directed action is told in Präsens like
Ich gehe Eis essen. Kommst du auch mit?
I'm going to get some ice cream. Do you want to come along?
(where the speaker had better said)
Ich werde Eis essen gehen. Wirst/Möchtest du auch mitkommen?
Even to me the second variant sound like distant future, so there seems no practical need to think of a tense for expressing future completed actions.
The example you chose is especially puzzling in its construction, because the main verb "fertig sein" has two parts and is based on the irregular conjugation of "sein". Please let me give you some more sentences to illustrate this:
Ich werde etwas morgen erledigen. (Futur I)
I will get something done tomorrow.
vs
Ich werde etwas morgen erledigt haben. (Futur II)
I will have gotten something done tommorow.
The Futur I case expresses the subject's determination to start the action tomorrow, while the Futur II case expresses the subject's determination to finish the sction by tomorrow.
To me, the concept and relation of Futur I and Futur II is like the relation between Präsens and Perfekt and between Präteritum and Plusquamperfekt.
This opinion stems from a Latin background, where the relation is even more emphasized by the composition of the conjugated form. See e.g. this source.
The difference lies with the point of view you assume when looking at both situations.
In the first one, you linguistically imagine yourself in the future, expecting what was scheduled to be ready is in fact ready then. This grammatical construction in German is called Futur II.
In the second one, in contrast, you portray yourself to be in the present, asserting that in the future the completion of what needs to be ready then has in fact occured. This piece of German grammar is called Futur I.
Both of them form together the canonical way of addressing the future in German. Futur I when looking at it from the present. Futur II when looking at it as the past from a future beyond that point in time.
Futur II is considerably less common in everyday language these days, whereas Futur I can be found with virtually all instances of everyday communication in the present.
Das wird bis Freitag fertig gewesen sein.
This is Futur II tense, which is —despite its name— not about the future. It's about conjecture. This example sentence in fact talks about the past, because the phrase gewesen sein can never be about a future event.
This had been ready by last friday. I guess.
Other verbs behave much nicer:
Das wird bis Freitag fertig gemacht sein.
Das wird bis Freitag getan sein.
These are guesses about the future, in Futur II tense.
Das wird bis Freitag fertig sein.
This is Futur I. Not a guess, but an announcement.
I disagree with all three afore mentioned opinions on the future II. I am also not aware of any formal references.
I find your example wrong, too, that is not idiomatic. Let's look at a different one.
Das wird für eine lange Zeit das letzte Mal gewesen sein ref
The perfect, gewesen, requires the event lie in the past.
Werden is treated as a suplement for future in the paradigm to be and at the same time as a present tense headword that has the lexical aspect of progress, including future.
The future aspect does not strictly apply to the perfekt participle. I find it practical to exclude that notion over all, thus finding your example invalid.
There is simply no need, because something that will have happened after now will always be a future tense anyhow. Wheras there's good use for a tense expressing that the current state of things will remain as is. A future tense above that, expressing a future state that would remain, would use would, or some other case of conjuctive irrealis/potentialis.
PS: Nevermind that I'd prefer to write Mal without capitalization, because das does not command a noun, if it is read as preposition, and mal can thus act advarbially and morphemically as it usually does, less obviously so in idioms like this one.
PPS: I would consequently recommend
Es wird Freitag fertig geworden sein
which strikes me as a bit more natural for what you were trying to say, though it's still clumsy. On one hand, as I tried to point out, it's redundant to the normal future, wird erledigt sein, "will be done".
