One way to check if a system is under invasion is by simply plotting a route. The game will mark a system under invasion as a colored, upside-down triangle on the jump queue, instead of the usual colored square.
It’s still pretty active. You have faction warfare people in the usual regions like Black Rise. Still quite a handful of solo and gang PVP players scattered all over. You’ll also find some PVE players mining, exploring, and doing missions.
I’ve only come back to EVE 4 days ago after being gone for 2 years myself, but one of the major additions I’ve seen aside from the invasion is Abyssal Deadspace. It’s a new type of combat PVE content. It also carries a higher risk (and reward) system with it compared to your usual PVE activity.
For simplicity’s sake, a player will generate an instanced “dungeon” from items that will open portals called “filaments” where they have 20 minutes to go through 3 rooms filled with Triglavian NPCs. That means that in that amount of time, you have to defeat the guardians lurking inside, and destroy and loot as much of the “chests” as you can. It also means that if you don’t go through the entire dungeon in 20 minutes, you lose your ship as well as your capsule. It has a similar random loot generation system as relic and data sites. These “dungeons” can vary in tiers. Tier 1 is the easiest with Tier 5 being the toughest, but the loot scales along with difficulty.
I’d tell you more but the link I provided will give you a more in-depth explanation.