Inspections when buying a home with deferred maintenance

We're buying a nice, upscale home that had a lot of deferred maintenance. For example, the HVAC systems are all 29 years old. Still functional but on their last legs. We priced that into our offer, along with other items identified on their disclosure. They've also used reputable local vendors (probably the same ones we would have used) for presale inspections and disclosures. They did all repairs noted in their disclosures (scattered minor dry rot, pool equipment, etc.), but didn't address the items still working but at or past the end of expected life (HVAC, pool surface)

We're definitely doing a general inspection and a pool inspection. What other inspections would you want to do in that situation?