Its been mentioned here numerous times and I couldnt agree more. I really dont understand why a heirloom pack counter has not been added. The counter is clearly already there in the background, as it's guranteed on number 500...
There are 3rd party sites that can give you a rough idea of where you are in the countdown to your heirloom, like the one below
https://apexlegendsstatus.com/apex-pack-calculator
The new(ish) level cap in Apex Legends is effectively 2000. You can loop through levels 1-500 4 times.
The total number of packs you can now earn, through leveling up to 2000, is 544 packs. That is a guaranteed heirloom.
Fyi for heirloom purposes, Thematic packs are the same as Apex packs, they count towards the 500 pack heirloom guarantee, while Collection event packs are different, as they just count towards the collection event reward and not towards the heirloom gurantee.
Recently published Heirloom Shard drop rates indicate an actual drop rate percentage of 0.045%.
https://answers.ea.com/t5/News-Game-Updates/Apex-Legends-Minimum-Global-Drop-Rates/m-p/14143089#M192