How frequently can / should I swim?

I’m looking to get into triathlon this year after a background in marathon running.

I’m comfortable with the cycling aspect, but I’m brand new to swimming (I wasn’t very good as a kid, and didn’t swim again until the start of the year – I’m in my early 30s)

I’m taking lessons once a week, and working on my technique, but conscious that one of the main things is just more time in water. Coming from a running background I’m very conscious of the risk of over training causing injuries and was wondering how much of a risk that is when it comes to swimming?

At the moment a typical week of training looks a bit like

M – Rest / Strength

Tu – Swim lesson & Run

Wed – Bike

Th – Run & Strength

Fri – Swim & Bike

Sa – Bike

Sun – Run & Swim

Time not being an obstacle, is it safe / advisable to put more swims into my week in order to progress? Or do I run the risk of over training? Should I just be patient and trust the process?

Would also welcome any advice for a beginner swimmer in the world of triathlon – I feel like I know what the proper technique and can do the various aspects in isolation, but am struggling to bring it all together at the same time at the moment!

Many thanks.