Can confirm this bug occurs in both 1.15.2 & 20w09a. Also found a case in which this issue doesn’t occur.
Tested with dogs & cats in singleplayer (1.15.2 & 20w09a):
Outside of spawn chunks this issue occurs as described within this bug report. Leashed standing dogs/cats teleport to the player when the world is loaded and the player is 20~ or more blocks away from their pet. (bug occurs)
Inside ‘fully loaded’ (often referred to as Entity Processing) spawn chunks, standing dogs/cats that are leashed do not teleport to the player when the world is loaded and the player is 20~ or more blocks away from their pet. (bug does not occur)
Issue occurs as described within this bug report when the pet in question is located at the edge of spawn chunks. i.e. In the Non Entity Processing chunks and Memory Loaded chunks around the edge of spawn chunks. (bug occurs)
Turns out this issue is similar to MC-245910 which was just fixed in 22w05a.
This issue is now (mostly) no longer present as of 22w05a.
Running the performance test again in 22w05a will still see the spikes in the TPS graph, however a spike will only appear every 10 seconds instead of the continuous spikes as seen in versions 1.18-pre6 to 22w03a. It appears that in 22w05a when a chunk experiences changes it will only be auto-saved as frequently as every 10 seconds now. Scenarios such as running a small storage system sees performance return to around where it was in 1.18-pre5.