For the hole I would go about 0.1 mm larger in the hole D, unless it is holding engine pressure.
Charts say 0.0960 - 0.0980 steel.
2,43 mm
2,48 mm
0.0890 - 0.935 in brass, alu, plastics.
2.26 mm - 2.37 mm
Disagree a bit with most posts re: form tap and no hand tapping.
In this particular case only, of making a single piece with major value in work done before tapping.
Form tapping (machine) with the right tools, in tap, fixture, and driving, will certainly thread the 2.4 mm hole 3 mm deep in about 2-3 secs, and can probably do 1000 holes before needing a new tap, success rate 1/1000.
Because:
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4-40 is sub-near 3mm.
In SS I would always hand tap it, in the OPs position of making a one-off with no sophisticated gear.
Using a machine tap, from any industrial supplier, with a brand.
And a hand held tap wrench.
Because by hand, You can easily feel binding and jamming, before the tap breaks in the hole.
By hand, I find I can back off, clear chips, carefully try to ease past a jam, back-n-forth, and it mostly works, maybe a 95% success ratio on deep difficult blind holes in SS.
Note deep and difficult, note SS, I would expect easy steel to have 99.x% success rate.
Spiral flute taps are great and have lower friction and resistance, tap easier.
But when they jam they also snap much easier.
Over 17 years of building cnc machine tools, and tapping maybe 13.000 holes, steels, 98% in F1 calibrado (basic tool steel), I mostly power tap with cordless drills, (5) 6-12 MM d, TYPICALLY 3 - 3.5 D deep to clear the tapered tap end and leave a bit of space for chips.
So for 6 mm // 1/4" I aim for 20-24 mm deep holes, and drill-tap them until the tap hits the bottom.
Success rate is about 2-3 breaks in 600 holes.
And I know perfectly well a 6-9 mm deep thread is enough in theory, but 1-2 threads at top may get weakened or buggered, and the last 8 mm or so are not fully formed with just one tap.
And the machine taps are gently tapered and prefer a deeper hole and some clearance.
And the machine taps or industrial std taps are quite resistant to twist, they wont break easily inside the SS workpiece, by hand.
Yes, if one runs the taps fast by drill or by spindle, the resistance is maybe half/0.75 vs hand tapping.
But hand tapping saves breakage.
My personal experience has been that SS does not work harden significantly.
But it heats, fast, a lot, and the drill binds due to heat expansion.
On 303, 304, 316L, upto 6/120 mm, or 16:1 D/L ratio, very deep holes.
Or 10/120 mm 303 SS, 12:1.