Considering the short distances involved, it's very odd they cannot find anything by a quick drone or aerial search. If he was injured and incapacitated, he could not have gone far either. The terrain also looks very sparse without trees and vegetation.
Also find it a bit strange that one person would choose to leave a group at a beach on the grounds of "being tired", only to undertake a walk in blistering heat without a cell phone. It feels like there's definitely information that they have not released.
The most logical thing in the same situation is for a couple to leave together if one isn't feeling well. Considering they already had a swim and enjoyed a bit of the beach, if one partner is tired then both would make their excuses and leave. And it seems crazy that you would let your husband (tired or unwell) walk home alone in 30+ heat without checking he had his cellphone.
It feels like he didn't want to be reached or he insisted on going home alone or there was some incident or argument that resulted in the solo departure. The 6 hour delay is also suspicious because considering the size of the island and the beach, it's quite unusual to stay that long in one location. The beach is idyllic but tiny. Considering they already had a swim and were there for maybe 1-2 hours after landing by boat, it meant the remaining group sat on a beach for 7-8 hours in the summer heat?! No matter how good friends you are, can 3 adults entertain themselves for 7 hours straight in one location? Especially considering one left after claiming to be tired/unwell, it would be bleedingly obvious to get home earlier and check on him.
Another giant question mark is why they did not attempt to call his cellphone after the time he should have been back at the villa, and why they chose to stay for at least several more hours on the beach after not being able to reach him. The walk was only 20mins, so they must have sent a message or attempted to call. Even if they assumed he might be sleeping, it should have raised alarm bells if there was still no call back after several hours.