Nightmare bedtime routine, how do we get out of it?

Hi everyone, I'm looking to get some advice please on how to get out of our nightmare bedtime routine with our eldest daughter aged 2 years and 10 months.

We've always been very strict at getting into a routine and it's worked really well for us so far. She slept 12 hours through the night from 3 months old, has always loved food and never said no to anything, and has generally been "easier" when compared with other kids her age. She's very smart, strong willed, and in the 99% for both height and weight. However, at some point in the past year, it happened gradually rather than suddenly, her bedtime routine has become unworkable.

She sleeps in her own room, which we also use as an office, in a cotbed with the sides still on. We've haven't taken the side off yet and turned it into a normal bed because shes never tried to climb out and it just works for us.

We've also just had a newborn, 2 weeks old, which is making life harder, although big sister hasn't yet shown any sign of negativity to the new arrival. Mum had a c-section so Dad is doing the bedtime routine, but even before the recent arrival the problem existed with either mum or dad.

Previous routine

17:00 - Dinner
18:00 - Quiet time, TV on, Bluey or similar
18:15 - Bathroom to give her a quick wash, or a bath depending on day of the week
18:30 - TV and small glass warm milk
18:45 - Brush her teeth
19:00 - Carry/walk her to bed, quick hug, lay her down, walk out, asleep within 5-10 minutes

Current routine

17:00 - Dinner
18:00 - Quiet time, TV, Bluey or Blippi usually
18:15 - Attempt to take her to bathroom, "1 more minute!"
We give her another minute, then its again "1 more minute"
I turn off the TV and threaten her, she ignores me, and goes to play with her toys
This continues for a while
18:40 - Finally get her in the bathroom, either a quick wash or bath is hard work, extended, or just doesn't happen
19:00 - Living room, small glass of milk
19:10 - Try to brush her teeth but usual routine of "1 more minute" repeats for 10-15 minutes
19:20 - Finally brush her teeth
19:25 - Try to take her to bed but again lots of "1 more minute" and screaming
19:40 - Eventually get her to bedroom but then the fun begins....
She will do anything to run away back to the living, and will do this multiple times
On repeat, I need a drink, I need to pee, need to wipe my nose. I take her to the bathroom only for her to then say "I don't need to go". All this will repeat multiple times.
20:00 (usually) I'll eventually get her to lay down in bed.
Multiple repeats of twinkle twinkle, Mary had a little lamb etc
I try to then say goodnight and walk out to get repeated screams and begging to stay.
I then end up sitting on the floor for 10-15 minutes holding her hand, singing nursery rhymes
Eventually I walk out for her only to scream that she needs "a quick hug"
All of the above then repeats for a second time
20:30-20:45 - It's eventually finished, I've left the room, and she's asleep.

When she repeatedly runs back to the living room I've tried picking her up, practically throwing her into bed and then walking out. She screams for 20 min+ before I go back in and hug her. This reduces the whole "routine" by a little but it's not a long term solution.

When she was younger we sleep trained her by doing 5/7/10 and just walking in, laying her down, then walking out again, and always before the 10 min were up she would be asleep, but it isn't working this time around.

I know that this is our fault by starting all the singing and hugs, but it's been gradual and after 6 months+ it's mentally draining.

Any suggestions?