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What kind of force commitment would be need for the Imperials to consider a space battle to be a major engagement?

More than 3.

I would have thought anything more than a couple of capital ships apiece, I.e. a standard BFG engagement. Anything less is an anti-piracy action

I would think it's about the value of where/why the fleet is fighting. Don't get me wrong, two big fleets fighting each other is a big engagement but imho it won't be a 'major' engagement if they are only duking it out in empty space of little importance.

EDIT:

 Flinty wrote:
I would have thought anything more than a couple of capital ships apiece, I.e. a standard BFG engagement. Anything less is an anti-piracy action

Forgot to put in the force commitment, my bad. Flinty pretty much hit the mark, though I don't think capital ships are necessary (but exciting to have) to make an engagement seem major.

Anywhere a Tyranid Hive Fleet is headed that intersects with someone else. Other than that, depends on the fleet. Each Sector has subsectors, which has yet more divisions. It all depends on what is there. But anywhere there is a fleet that intersects an enemy fleet, it is a major engagement to someone. Exterminatus missions automatically count as major engagements.

Probably any time that both sides of the battle are fielding at least 1 capital ship and its escort vessels would be considered a "major engagement", because vessels of this size and class are rare, and can unleash god-awful amounts of devastation.

Ship numbers in 40k is rather small due to their size and complexity. Probably over 5 cruiser class vessels

To describe an engagement as "major", one could use classification listings as described by the military.

If the destruction of the involved ships would result in catastrophic loss of life or resources for the nearby system(s) then I would classify it as a "major" engagement. If the destruction of said vessels would only result in diminished productivity and proportionally "acceptable" casualties, then it could be seen as a "minor" engagement.

You could expand system(s) to include fleet logistics, but at that point you are still required to narrow your scope to make your overall determination as to how significant the engagement was. In the scope of the entire galaxy, the loss of a few capital ships is very minor. However, if those are the only capital ships within a three month travel range, then that particular area is going to suffer a great deal until reinforcements can arrive. Mobility of a set number of resources and the required maintenance and supplies for these vessels must all come into consideration.

We on Earth have a much easier time describing our maritime, land and air conflicts as major or minor. We are aware of our finite resources and the overall impact that the loss of these resources will have on our abilities to effectively conduct war.

Sorry if this just convoluted the question, just my few cents.

I imagine a naval task force would have to be involved for it to be a fleet engagment.