2nd Opinion on AC repair
I can purchase a new 25 lb cylinder of R410A online 160$
Brand new 5 ton outside unit 1700.00  includes shipping.
how many ton is the system? Goodman is a low cost system but if properly installed it should last 10+ years,
If there is a leak it was small the system is still cooling right.
you wanted a second opinion if the unit is smaller the cost is less. The outside unit includes the compressor, controls, coil, fan etc.
A coil would be much less expensive.
I smell a scam just saying.