Speaking of Strucker suspecting Captain America was "one of them," we have to mention his other purpose for coming to New York. Recruiting Luca was just a side quest.
His main objective was to retrieve a gift sent to him by "Captain America."
Loki's Scepter.
This goes back to the immediate aftermath of the First Battle of New York.
Hydra agents embedded in SHIELD (the STRIKE team) had initially recovered the Scepter.
They were preparing to hand it over to their faction leader, Alexander Pierce. But then, Captain America intercepted them in an elevator, whispered "Hail Hydra," and walked away with the Scepter.
This incident caused a massive, silent earthquake within Hydra's leadership.
Captain America knows Hydra exists.
Captain America claims to be Hydra.
Captain America didn't expose Hydra afterward.
Any one of these facts was explosive. Together, they paralyzed the organization with paranoia.
Initially, Hydra's various factions investigated each other.
Pierce knew he didn't recruit Steve Rogers. But Steve knew Pierce was Hydra. He knew Crossbones was Hydra. He knew secrets that 99% of Hydra agents didn't know.
If Pierce couldn't figure out who turned Cap, he couldn't sleep at night.
However, after extensive investigation...
Hydra concluded that the "Captain America" in the elevator was actually Loki using illusions.
Sure, Loki knowing about Hydra was bad, but it was better than Captain America actually being a double agent (or a threat they couldn't control).
So for a long time, while SHIELD hunted Loki, Hydra was secretly hunting him too, desperate to silence him before he spilled their secrets.
However...
When Hydra finally made contact with the real Loki and formed an alliance, Loki demanded the Scepter back. And Loki clearly didn't know much about Hydra's internal workings.
This threw the "Loki disguise" theory out the window. The identity of that elevator-Cap became a mystery again.
The only reason the "Loki disguise" story held any water was because the real Steve Rogers claimed it was Loki. But with the surveillance cameras in Stark Tower destroyed, no one could verify the truth.
Hydra's leadership was back to panic mode. A sword of Damocles hung over their heads.
But that was Pierce's perspective.
Baron Strucker knew something Pierce didn't.
On the same day the battle ended, a "Captain America" appeared at a secret Hydra base in New York, dropped off Loki's Scepter, and vanished without a trace.
And this base happened to belong to Strucker's European faction.
The base commander immediately locked down the facility and contacted Strucker for instructions.
Strucker, paranoid that it was a trap or a test from rival factions, sat on the information. He waited until now to come collect the prize personally.
In Strucker's mind, the Captain America who delivered the Scepter was likely an ally. But caution dictated he verify Steve's loyalty further.
What Strucker didn't know was that since leaving the Aurantius Villa, his every move was under Luca's surveillance.
"So that's where the Scepter went? Steve really did a sloppy job."
Luca, having pieced together the truth from surveillance feeds and intercepted comms, shook his head at the timeline shenanigans.
He wasn't blaming the current Steve Rogers, who was busy being a model hero.
He was blaming Old Steve from Avengers: Endgame.
That "Hail Hydra" scene was cool in the movie. But in reality, it left a massive mess for the present-day Steve to clean up.
If Captain America wasn't such a public icon, Hydra would have kidnapped and tortured him for answers already.
And more importantly, Old Steve just handed the Mind Stone to Strucker?
"Restoring the timeline doesn't mean literally giving the villain the super-weapon..."
But complaining aside, this was good news for Luca.
"I was planning to use Strucker for a while, but now... I don't need him."
Luca's eyes narrowed as he watched the screen.
He had considered killing Strucker and replacing him using the [Transformation Watch].
But the watch only copied appearance, not memories. A fake Strucker who didn't know the passcodes or the layout of his own base would be exposed instantly.
But if Luca got his hands on Loki's Scepter (the Mind Stone)?
Controlling minds made taking over Hydra's European branch "Easy Mode."
"I don't know where Old Steve got the Scepter—didn't he only bring the Stones back?—but whatever. A free Mind Stone? It would be a waste not to take it."
In Luca's eyes, the Mind Stone was now unowned property. Finders keepers.
Decision made.
Luca stared at the monitor and issued a command to Haro.
"Aurantius Haro. Execute the operation."
On the screen, a small black dot zoomed across the azure sky.
It was rapidly approaching another dot—the private jet carrying Baron Strucker back to Sokovia.