“Stitching” a nap together

My daughter is 14w now and we’re going through that cat nap phase where she will sleep no longer than 20-30 mins at a time for her naps.

She’s pretty good at night, sleeping 8-10 hours most nights but the cat naps in the daytime make the 2-3hr run up to bedtime miserable because she seems very over tired.

She’s not long finished a nap but was clearly still tired despite being seemingly wide awake. So I’ve fed her and put her down again and she’s semi-asleep again now, i don’t know if she will sleep or not I’m just seeing what happens.

What are other moms thoughts on this? If she’ll sleep go for it? Or once she has the 30 minutes am I best trying to stick with a set wake window and trying again?

I don’t want to ruin her night time sleep but equally I want her to feel refreshed during the day and these short cat naps aren’t doing it 😅