I doubt this is an issue.

Not because wind wouldn't affect an empty booster; it certainly would.

But since the booster returns within 8 minutes of the launch, the weather in which a booster lands is restricted to the weather in which they will launch a rocket.

But then wouldn't the limiting factor for launch be the maximum allowed wind for landing?

The value of what is going up (which includes the booster) will be greater than the value of the empty booster. Factors of safety would be based on the launch rather than the catch. In other words, if it's deemed safe to launch the calculation for safe to land is easier to pass. Especially when you are taking passengers on launch. Wind is already a significant factor in launch.

That's true, except it neglects the cost of the launch tower itself. If you botch a catch and need to rebuild the launch tower, that could get very expensive, both in immediate costs of rebuild, plus in opportunity cost of missed launches. So in the end, whichever has the lowest wind limit, launch or landing, will likely determine whether they fly.

Ah, excellent point! They wouldn't ignore one hazard because another is less severe. And you are correct, I wasn't considering hazards to the launch tower itself. I think you are absolutely right, either would cause a flight to be scrubbed. I wonder if the two wind limits would be different.

That value is unlikely to be significantly different than safe takeoff conditions. Yes the booster is lighter at landing, but launch is way more dangerous with larger error margins and more conservative condition requirements.

This is often the case with airplanes; it's not a new concept.

Definitely not, and I am not trying to be a doomsayer here. It's just interesting. Now that I think about it more, I believe a Falcon 9 Starlink launch was once delayed due to weather conditions at the drone ship.