Yes, it is a bit too strong
You essentially gain the approximate benefits of a feat like Dual Wielder.
The light weapon limit to two-weapon fighting could essentially be bypassed with this system as you could use a higher damage weapon and still get an attack with your bonus action.
This is comparable to the weapon expansion portion of Dual Wielder.
Also, to add the ability modifier to a second attack you would usually need to select the correct fighting style, but your variant ignores this.
This is comparable to the Armor Class portion of Dual Wielder. (A fighting style level benefit, i.e. the Defense Fighting Style)
The only other concern is that you could split up where you attack and have a hand free, but that will rarely be important.
Does Beastmaster Ranger deserve the benefit?
I am of the opinion that granting a free feat-level bonus to Beastmaster Ranger pushes it above the power level for the other classes.
If you treat your modified character as a dual-wielding fighter for analysis purposes, it deals comparable damage but trades (pre-level 10):
- Action Surge
- Second Wind
- Martial Archetype features
While the fighter is clearly better combat-wise, the ranger compares due to its out-of-combat utility. The free fighting style and better weapon option makes it too strong.
After level 10, ranger features becomes even better with their higher level spells and since travel is more important in later tiers when dealing with threats of greater magnitude (as evident by the appearance of spells like teleport). Getting one more attack and one more archetype feature for the fighter doesn't compensate.