You worked faster than I typed! Glad it came out ok. Glad the 13/64 dill worked. Generally, 3in1 or WD40 DON'T work as well as tap cutting oil, but this is water over the dam now. And for a through (and not a blind) hole, a tapered tap is fine. Running it into the hole to the point where its not tapered is what you want to do.

Typed before I read what you'd done:

Just a point of correction: the nominal correct size for an M6 cutting tap is often given as 5mm. That's for 100% thread depth. As a nod to practicality, most holes drilled for tapping specify about 65-70% of full thread depth. That's where you 5.2mm comes in (one formula is drill size = nominal thread OD - Percent thread engagement/76.98). A bit more accurate estimate using the formulas in the webpage below is between 5.1556 and 5.089mm. But here's the thing: if you use a hand drill, and/or a poor quality drill bit, your hole diameter is going to be larger than the drill. I would target a little less than the 5.09-5.16 target. For this reason, I'd use a number 8 drill (note that this is a NUMBER drill, and the number 8 is not mm). Or a number 7 drill if I had it. But you'd probably be fine with a 13/64 as well. With a number 6 drill of good quality and steady hand you'd be close, but still be too big for my taste. It might work. Use tapping fluid (normal oil doesn't do as good a job).

The penalty for too big a hole is a weak threaded connection. For too small a hole is difficult tapping and possibly a broken tap.

The advice above is for tapping into steel. If you have a notion to try your hand and at tapping titanium, my suggestion would be ... don't. Even drilling Ti can be problematic - it work hardens something fierce and the drill tends to wander as a result. Get someone who's done this. If you must, read up first on drilling Ti, then on tapping Ti, and do some research and get a really good drills and taps. Emuge, Prototyp... etc. And use moly-dee or some other good lubricant.

No. 8, 5.05mm, 0.1990 inch
No. 7, 5.11mm, 0.2010 inch
Fractional 13/64, 5.16mm, 0 .2031 inch
No. 6, 5.18mm, 0.2040 inch

For tap drill sizes:
https://www.natool.com/wp-content/up...atp113-116.pdf
For available drill sizes:
https://www.imperialsupplies.com/pdf...DrillChart.pdf