How to summon a slime as a marker

Marker can only be used with armor stands.

To prevent your slimes from suffocating you can use the Invulnerable tag instead, it would look like this after adding it to your command:

/summon slime ~ ~-1 ~ {CustomName:'{"text":"oC.Slime"}',Glowing:1,NoAI:1,NoGravity:1,Size:1,Invulnerable:1}

This is as close as you can get to using the Marker tag on slimes. They will still have a hitbox, but they cannot be killed, unless you are in creative mode. They won't have any AI, or gravity.

If you want to prevent an entity from dropping loot, then you can use the DeathLootTable tag. It doesn't seem like smaller slimes get that tag from their parents, but you could use it on a slime with Size:0:

/summon slime ~ ~-1 ~ {CustomName:'{"text":"oC.Slime"}',Glowing:1,NoAI:1,NoGravity:1,Size:0,Invulnerable:1,DeathLootTable:"minecraft:none"}

Markeris not a tag that slimes can have. It's a tag for armour stands, which are much easier to handle. The classic marker armour stand is summoned like this:

/summon armor_stand ~ ~ ~ {NoGravity:1,NoAI:1,Invisible:1,Marker:1}