How does the Mobile feat interact with the Writhing Tide for a Swarmkeeper Ranger?

In the Swarmkeeper section for Rangers in Tasha’s Cauldron of Everything there is an ability called Writing Tide (TCoE, p.60), which allows the Ranger to fly.

Writhing Tide

7th-level Swarmkeeper feature

You can condense part of your swarm into a focused mass that lifts you up. As a bonus action, you gain a flying speed of 10 feet and can hover. The effect lasts for 1 minute.

You can use this feature a number of times equal to your proficiency bonus, and you regainall expended uses when you finish a long rest.

In the Player’s Handbook the feat Mobile (PHB, p.168).

You are exceptionally speedy and agile. You gain the following benefits:

• Your speed increases by 10 feet.

• When you use the Dash action, difficult terrain doesn’t cost you extra movement on that turn.

• When you make a melee attack against a creature, you don’t provoke opportunity attacks from that creature for the rest o f the turn, whether you hit or not.

Does this mean that if you take Mobile as a feat, the benefit would apply to this particular feature too – effectively having a fly movement of 20 feet instead?