So basically I was getting annoyed that Serana was setting off traps and would be discovered all the time by enemy NPCs (despite having an in-game sneak skill of 98).
And I like Serana as a character and follower so I wasn't privy on going at it alone.
So I gave her some perks, not only stealth ones but some combat ones as well that should hopefully make her more powerful/useful while not making her overpowered.

The perks I gave her are: 

Magic Resistance Rank 2 (she starts with rank 1)
-20% magic resistance

Dark Souls 
-100 health for summoned creatures

Light Foot
-Will not set off pressure plates

Armsman Rank 1
-20% more damage with one handed weapons

Stealth Ranks 1, 2, and 3
~30% harder to detect)

Bladesman Ranks 2-3 (she starts with rank 1)
-Extra chance to grit (20%) with extra crit damage (+50%) with swords

Hack and Slash Ranks 2-3 (she starts with rank 1)
-Makes enemies bleed when attacked with axes

Deep Freeze
-Low health enemies are paralysed with frost spells

Silence
-Running doesn't affect sneaking

She already starts with Custom fit and fighting stance as well.

Hopefully this will make her a bit more useful while also keeping it reasonable. It isn't a perfect fix for the whole "I'm an NPC and the minute my leader has any potential danger I will rush in!", but hopefully it should be a little better.

The mods that make her look like the pictures are TCM (https://www.nexusmods.com/skyrimspecialedition/mods/1037/?tab=description) overwritten by CBBE Slim (https://www.nexusmods.com/skyrimspecialedition/mods/198/).

Compatibility:
I didn't rip out the default Serana appearance from the ESP, so this will conflict with mods that change her appearance. As it is a simple ESP, however, you should be able to load this first and have any of your appearance mods overwrite this file's appearance data.