So I started trying to test different numbers in turn-based mode to try to get a handle on how Dexterity, armors and attack speed bonuses affected initiative gain turn-based mode. I posted the results on the /projecteternity reddit first (which can be viewed here), but then I realised that folks who really know the game's mechanics well are probably here.

I'll post a summary of my main findings.

After I posted my initial results, Selroy46 went ahead and dug up the actual formula used in the game code:
"(2 (base attack time)/(1 + (Dex - 10) / 33.3) + 1) (1 - 2 * (sum of all speed bonuses and penalties)) / 1.2

This value can't be less than 1.0." - Selroy46
Caveat 1: Includes a -0.5 speed penalty if not dual wielding.
Caveat 2: This recovery is applied to each attack when dual wielding, depending on the weapon being held. If both weapons have the same speed, then x2 essentially.
Consequently, dual wielding is VERY sensitive to non-Dex speed bonuses and penalties, including armor penalties.

Anyway, by assuming no attack speed bonuses we can use an abbreviated formula to see the benefit of Dex using the formula of Recovery = (2 * (base attack time)/(1 + (Dex - 10) / 33.3) + 1)/1.2:

Dex	TBM Recovery time	TBM Recovery increase	TBM Marginal Recovery increase per Dex point	TBM Marginal Speed increase per Dex point
3	117.7%	-17.7%
4	114.7%	-14.7%	3.1%	2.3%
5	111.8%	-11.8%	2.9%	2.2%
6	109.1%	-9.1%	2.7%	2.2%
7	106.6%	-6.6%	2.5%	2.2%
8	104.3%	-4.3%	2.3%	2.1%
9	102.1%	-2.1%	2.2%	2.1%
10	100.0%	0.0%	2.1%	2.0%
11	98.1%	1.9%	1.9%	2.0%
12	96.2%	3.8%	1.8%	1.9%
13	94.5%	5.5%	1.7%	1.9%
14	92.9%	7.1%	1.6%	1.9%
15	91.3%	8.7%	1.6%	1.8%
16	89.8%	10.2%	1.5%	1.8%
17	88.4%	11.6%	1.4%	1.8%
18	87.1%	12.9%	1.3%	1.7%
19	85.8%	14.2%	1.3%	1.7%
20	84.6%	15.4%	1.2%	1.7%

And that's the benefit of Dex! It's no longer 3% per point due to how it works in TBM.
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Next, some recommended Dexterity breakpoints

While wearing armor, one should normally expect to go only once per round, i.e. every six seconds. Assuming an average speed melee one-handed weapon (or fast ranged weapon or slow two-handed weapon), I can recommend some Dex breakpoints

- Dex 8, Robes (-0.15): TBM recovery = 5.99s

- Dex 10, Padded (-0.2): TBM recovery = 6s

- Dex 12, Hide (-0.25): TBM recovery = 6.01s

- Dex 14, Leather (-0.3): TBM recovery = 6.04s

- Dex 16, Scale (-0.35): TBM recovery = 6.06s

- Dex 18, Breastplate (-0.4): TBM recovery = 6.1s

- Dex 21, Mail (-0.45): TBM recovery = 6.05s

-Dex 24, Brigadine (-0.5): TBM recovery = 6.02s

Durance has Dex 9 and wears robes by default, whereas Aloth has Dex 15 and wears Leather by default.

Using Dex to act gain mulitple actions per round is tricky. To hit 5s intervals with armors with an average weapon, these are the Dex scores you need assuming no other bonuses to speed.

- Dex 18, Robes (-0.15): TBM recovery = 5.01s

- Dex 21, Padded (-0.2): TBM recovery = 5.01s

- Dex 24, Hide (-0.25): TBM recovery = 5.02s

- Dex 27, Leather (-0.3): TBM recovery = 5.04s

-Dex 30, Scale (-0.35): TBM recovery = 5.06s
And so on.

Attack speed works a LOT better to gain more attacks per round, but it's there's some confusion about how it's added or not added so let's leave that for now.
The main breakpoint I found is that while dual wielding average melee weapons, Dex 20 and Robes, with Swift Aim (+20% attack speed) and Two Weapon Fighting Style (+20% attack speed) will drop the time between intervals to 2s. 2s seems to be the minimum interval.

Edited July 23Jul 23 by mrbunnyban
correcting table

(mistake, turns out I can edit my post)

Edited July 22Jul 22 by mrbunnyban