That was why I thought maybe making the second attack no longer count as a bonus action, but simply part of the normal attack action.
This is my homebrew version of Dual Wielder
Dual Wielder
You gain a +1 bonus to AC while you are wielding a separate melee weapon in each hand.
You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren't Light.
The two-weapon fighting attack you make with the melee weapon in your other hand,
doesn't require a bonus action.
You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one.
The third element is the changed part. It's not intended to allow two off-hand attacks, but only free your bonus actions for other things. An oversight, but I've never really thought about how this would interact with TWF style. It's giving your damage bonus to one attack... perhaps 2/3/4 by tier after accounting for accuracy. Slightly weaker the Dueling.
GWF is worse, probably, which says something.
For the record, I use the following fighting styles in my game:
Defense: AC +1, and +2 to all saves
Duelist: +2 to all attack rolls
Two- Weapon: +1 to AC and attack rolls, and add damage dice together for every attack.
Striker: Add proficiency bonus to weapon damage when using a weapon in two hands.
For me, those are too strong. For example, my players got the gift of Protection (found in Blingdenstone, in OOTA) which is like a Ring of Protection. One of them later found a Luck Stone, and another got their hands on an actual Ring of Protection. What I then found when estimating encounters for them is that I had to count them one or two levels higher for the DMG guidelines. Your Duelist is crazy-strong. I mean, look what Archery does with Sharpshooter. Your Duelist can stack onto GWM...
GWF is perhaps the poorest fighting style, so of what you have I feel l like Striker is most justified. It is intentional that it will apply to both melee and ranged weapons, right? My take -
Archery - strong as written
Defense - good as written
Dueling - could be 1d4 instead of +2
GWF - not sure, seems
very bad as written
Protection - not sure, seems bad as written - might be okay if it
didn't use your reaction
TWF - not sure, seems bad as written
Two out of six seem good to me. One on the cusp. Two bad. One
very bad. So I do think DMs tweaking for their games is justified in the sense of broadening viable options. I don't think any fighting style needs to be stronger than Archery, and Archery is possibly a little too strong. I also think each style must be tightly worded to apply to the pictured *ahem* fighting style. So Dueling... must apply
only to a one-handed fighting style, etc.