It is what you don't include which is important!
Don't include: More playing with daddy or mummy, during bed time (other time is absolutely fine)
You don't have a routine to make them tired and fall asleep. You have a routine to let them know it's time for them to go to sleep. Subtle but different.
Think about what going to sleep would ideally be like when they are a bit older, and work to designing a routine like that.
Have a bath with them if you want to. You need to clean them at some point! It can be fun for them and can be a good one last hazzar for them before they go to bed. But it has nothing to do with getting your little one to sleep.
Reading can be similar. It is good for bonding and developmentally. Only reward behavior from them which you are happy with. If you are happy them clapping and giggling, then that is fine. But if they are getting you to chase them trying to calm them down, well they are just playing you!
So if they try running away, just stay with the book, tell them you are just going to keep reading by your self, and keep reading. Don't let them trick you into playing another game.
Ok now it's actual bed time Tell them something like "Ok it's sleep time now" Treat it like a you are just pointing out a fact that you both know. Not as a harsh command.
This is what I used to do, YMMV.
I would lay my little one down, give them a kiss say good night, say I love you and sing them a song. Actually I would play an Adele or Florence and the Machine, because I can't sing, holding my phone above them so they had to lie on their back to see it. I would slowly keep turning the volume down. Sometimes I would stroke one finger softly from the center of their forehead down their nose. This feels soothing and makes them blink and that helps make their eyes feel heavy.
Now this is the important part: I would lie on the spare bed beside the crib (and surf on my phone, but that's not the important part) and not interact with them. That is different than ignoring them. The goal is for them to feel safe that you are near by, but know you not are going to play anymore. Occasionally I would remind them 'It's sleep time now' if they try and interact with me. Treat it like you are reminding them of the fact, not telling them off. After 5 min I would get up and say 'I going to see mummy now, see you in the morning'. They don't need to be asleep before you leave!
If need be, remind them you won't be far away. If they cry do not reward that with extra cuddles. Pop back in and say 'It's ok, I love you but it's time for you to lie down quietly now' and head back out. The goal to NOT to let them cry themselves to sleep, but also don't let them 'play you', for extra cuddles. With extra 'you time' and sleep you will be able to give them better cuddles etc during the day.
After a short while of doing this going to bed only took about 10min (Most nights at least 😜)
Also explain to them what you are doing as you go. They can't communicate well yet but you can still include them in what is happening and why you are doing things.