We are using Tealium to serve our tags, including the GST, identified in Tealium as "Google Ads Conversion Tracking & Remarketing (gtag.js)". This was the pixel Tealium configured based on the tag snipped provided by our marketing team.
I believe the issue is with Safari’s ‘Intelligent Tracking Prevention’ (ITP) and seems you are already using a suitable work-around by deploying on all pages. Albiet to piggyback that, see if you can identify UserAgent correctly within template logic and configure gtag mannually as per your requirements. DoubleClick would be my ideal suggestion for the tag container.
For the longer run, I would prefer to suggest introducing GTM for more flexibility.
Hope this might help.