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Yes for the event name. For the furnace ticker look at BlastFurnaceBlock.getTicker() and how its helper method creates a server side ticker for AbstractFurnaceBlockEntity.serverTick() The "litTime" in the BlockEntity would be equivalent to your ticks.

In 1.18.2 it is called WorldTickEvent I think if you subscribe to TickEvent you will get all tick events; server, level, player, etc. ? So you will get a lot more events than you want. As described above, you need to look at event.phase (either START or END) otherwise you will be doubling counting. Similarly, you might want to check event.side if you don't want your code to run on both the logical client and server, usually ticking is only done on the client to support things like animations. Finally, you can't store the ticking/ticks like you are probably doing. What if there are 2 blocks that you need to tick? What if somebody restarts the game while it is ticking. What is going to save/reload the ticking/ticks state? See the comments above about capabilities for how to solve this.

Normally there are 2 ways to get a block to tick. Use a BlockEntity (like a furnace keeping track of burn time) or have the block implement random ticking (like crop growth). You can also use the LevelTickEvent to implement more generic things, but for your usecase you will then have the problem of where to keep track of per block state. You might for example attach a capability to the LevelChunk that contains the block to hold the data? See DataStorage here: https://forge.gemwire.uk/wiki/Main_Page

The versions of mining gadgets, whisperwoods and baubly heart canisters that you have, have not been updated to work with the forge 1.19 recommended release. Check you have the latest version, otherwise you will have to wait for the mod authors to update them.