It’s hard to tell from that video alone but the lag spikes might occur as you get within loading range for player built structures, which should stabilize after they are fully loaded, is that not the case?
Having a PS4 Pro and the game installed to a SSD or external drive definitely helps with performance and loading the game/assets, but we’d suggest that you first try to rebuild the PS4 database and, if that doesn’t help, try and perform a clean reinstall of the game. Please let us know if either help.