Yes, ASAP Utilities 8.6, works with the new Excel 2024. 
Microsoft has scheduled to release the new Office 2024 later this year (2024).

We tested ASAP Utilities with the preview of Office 2024 that was released in April 2024.
This is a screenshot of ASAP Utilities with the preview of Excel 2024:


The exact Excel 2024 version that we tested ASAP Utilities 8.5 and 8.6 with is:
Microsoft Office LTSC Professional Plus 2024 Preview
Microsoft® Excel® LTSC MSO (Version 2404 Build 16.0.17531.20120) 64-bit

Office 2024 release date

Based on the current information and earlier release dates from Microsoft, we expect Office 2024 to be officially released in Q3 or Q4 2024.
(Office 2016, 2019 and 2021 were released in the months September or October.)