A raw or lightly-modified steel container is very unlikely to be approvable here. Three gates, in order:

Presidential Estates POA (hardest — start here). Your title commitment lists the Declaration (ORB 2453/1697, seven amendments) plus a Development Restriction Agreement (ORB 24647/1813). Communities like this almost always require prior written ARB approval and commonly prohibit metal buildings outright. Email the property manager before spending anything.
City of WPB zoning. Cargo containers are generally not permitted as permanent accessory structures in single-family districts. A habitable conditioned gym needs full permits: engineered foundation and tie-downs for ~170 mph design winds, impact-rated openings, electrical, and plumbing if you add a bath.
Engineering economics. Once engineered to code, a permitted 20ft container gym runs $45k–90k — no savings over conventional construction, with lower resale contribution. Steel also sweats badly here; closed-cell foam is effectively mandatory.

Option	Footprint	All-in	Notes
A. Site-built to match the house	12×20 to 14×28	$85k–175k	$60k–100k without plumbing. Best approval odds and resale.
B. Prefab studio (Studio Shed, Kanga)	10×14 to 12×24	$55k–110k	Confirm FL Product Approval and signed/sealed drawings for 170 mph.
C. Clad & permitted container	8×20	$45k–90k	Only if the POA says yes in writing first.
D. Open-air pergola gym	300–400 sf	$15k–40k	No habitable-structure trigger; much lighter ARB lift.

Free diligence, two weeks: email the POA for ARB rules; call 811 plus FPL locates for the transformer feed at that corner; take the survey to WPB Development Services and ask their stance on containers, accessory setbacks, height, lot coverage, and whether a half-bath needs its own sewer tie-in.