Complimentary exercises

Yes. Given how much tennis + pickleball + swimming you already do, you have a very specific imbalance: you get plenty of legs, rotation, pulling through the stroke, shoulder endurance, and cardiovascular work, but relatively little deliberate pushing strength, scapular/rear-shoulder strength, hip stability, and basic lower-body strength.

I would think of your gym work as “fill the holes,” not add more conditioning.

Your highest-value exercises

Exercise

Why it matters for you

Priority

Leg press

Quads/glutes; strength that tennis/pickleball don’t fully develop

⭐⭐⭐⭐⭐

Step-ups

Single-leg strength + balance + hip stability

⭐⭐⭐⭐⭐

Push-ups or chest press

Swimming doesn’t replace horizontal pushing

⭐⭐⭐⭐⭐

Face pulls

Rear delts, external rotation, scapular control

⭐⭐⭐⭐⭐

Seated/standing row

Balances repeated forward/overhead strokes

⭐⭐⭐⭐

Romanian deadlift

Hamstrings + glutes + posterior chain

⭐⭐⭐⭐

Calf raises

Important for tennis/pickleball acceleration and deceleration

⭐⭐⭐⭐

Pallof press

Anti-rotation core—excellent complement to all your rotational sports

⭐⭐⭐⭐

Lateral band walks / hip abduction

Glute medius and lateral hip stability

⭐⭐⭐⭐

Farmer carry

Grip, core, posture, shoulder stability

⭐⭐⭐

The ones I would add to your list

You already identified:

Push-ups + leg press + step-ups/StairMaster + face pulls.

I’d add these four:

1. Romanian deadlift

Probably the biggest missing movement. Tennis and pickleball involve enormous amounts of knee bending and rotation, but you don’t necessarily get enough controlled hip-hinge/posterior-chain strength. Use light-to-moderate weight and perfect form.

2. Row

A cable row or machine row. Swimming gives you a lot of repetitive shoulder movement, but a controlled strength-oriented row is useful for the upper back and scapula.

3. Lateral band walk

This looks almost ridiculously easy until you do it correctly. It trains the gluteus medius and lateral hip—the muscles that help stabilize you when you plant and change direction.

4. Pallof press

I’d choose this over lots of crunches. You’re already rotating your trunk thousands of times through tennis/pickleball. What you need is some ability to resist unwanted rotation and stabilize the torso.

And one important distinction

I wouldn’t count the StairMaster as equivalent to step-ups.

The StairMaster is primarily conditioning/endurance.

Step-ups are a strength/balance exercise. For your purposes, I’d actually favor:

8–12 controlled step-ups per leg × 2–3 sets

over spending a lot of additional time on the StairMaster.

Your “balance the athlete” workout

If you went to the gym twice a week, I’d make it surprisingly short:

A — Lower body

• Leg press — 3 × 8–12

• Step-ups — 2 × 8–10 each leg

• Romanian deadlift — 2 × 8–10

• Calf raise — 2 × 12–15

B — Upper body

• Push-ups/chest press — 3 × 8–15

• Cable/machine row — 3 × 8–12

• Face pulls — 2 × 12–15

• Pallof press — 2 × 10 each side

• Lateral band walk — 2 × 10–15 steps each direction

That’s only about 30–40 minutes, and I think it complements your sports considerably better than adding another generic cardio workout.

One other thing: because you’ve had that lower-back episode, I would initially make the Romanian deadlift very conservative and emphasize the hip hinge rather than chasing weight.

If you want, I can also  build you a “tennis/pickleball/swimming balance program” of only 8 exercises, ranked by importance, that you could do at Planet Fitness in about 30 minutes.