Pending availability of funds

The question of consideration seems irrelevant to everything.  Please, why are you asking about consideration?

The question of the protest clock depends on when you provided notice to unsuccessful offerors, or when they may otherwise have learned.  Did you provide notice to unsuccessful offerors close to the "CO signature date" or are you waiting until the "next FY effective date"?

contract questioner said:

In signing a contract this fiscal year, pending availability and with an effective date of next FY, are we actually providing consideration?

Yes, as long as there has been an exchange of promises.

Assuming that the solicitation contained the availability of funds clause, then, presumably, the offeror assented to that condition. The consideration provided by the government was its return promise to perform in accordance with the terms of the offer, conditioned upon the availability of funds. That promise is consideration even though conditional.

See Restatement, Second, Contracts § 76, Conditional Promise (1):

"A conditional promise is not consideration if the promisor knows at the time of making the promise that the condition cannot occur."

Emphasis added.

See also the discussion of conditional acceptance in Cibinic and Nash, Formation of Government Contracting, 4th ed., pp. 247-250, and the discussion of consideration, pp. 264-275.

contract questioner said:

Does the protest clock start with CO signature date or next FY effective date when funds are added?

Neither. Assuming that you are asking about a protest against award at the GAO, see 4 CFR 21.2, Time for filing (2):

Quote

(2) Protests other than those covered by paragraph (a)(1) of this section shall be filed not later than 10 days after the basis of protest is known or should have been known (whichever is earlier), with the exception of protests challenging a procurement conducted on the basis of competitive proposals under which a debriefing is requested and, when requested, is required. In such cases, with respect to any protest basis which is known or should have been known either before or as a result of the debriefing, and which does not involve an alleged solicitation impropriety covered by paragraph (a)(1) of this section, the initial protest shall not be filed before the debriefing date offered to the protester, but shall be filed not later than 10 days after the date on which the debriefing is held.