ArcGIS Pro 2.8.8 is binary incompatible with Pro 3.x. You cannot install 2.8.8 alongside Pro 3.0 on the same machine unless both are installed as side-by-side versions (which Esri supports by default, as they are separate applications).
: Obtain the ArcGIS_Pro_288_179344.msp (or similar executable) from the My Esri Downloads sub-tab. arcgis pro 2.8 patch 8 -2.8.8-
ArcGIS Pro 2.8 Patch 8 (2.8.8), released on , was a critical cumulative update designed to address high-priority stability issues and security vulnerabilities. ArcGIS Pro 2
If you are on 2.8.0 or 2.8.3, you might ask: "Why risk changing a working system?" arcgis pro 2.8 patch 8 -2.8.8-