So whats the problem. You already have everything laid out just put the cover over the stairway and add a pergola with a solid roof instead of shaded. It seems like you have plenty of room to accomplish everything you want.

Yours is a very generous sized patio which will enable you to accommodate most anything. Ours is approximately 24 x 26 with an additional 8 x 12 for a hot tub, 5 x 9 grilling space and a 12’ half-round firepit area. Pergola is 8 x 12 that seats up to 8.

Provisions for adjacent landscaping is equally important. We allowed 24 feet on both sides and trees there now shade the patio.

thanku for the response.. will a store bought pergola be strong? also my steps to enter patio are walkin stairs. how to do the roof over those stairs.
also any landscaping ideas around patio is appreciated.. I am not able to decide how to arrange fruit trees/ few shrubs. I'd also want to add few rocks in the landscape.. between plants.
thanku

https://youtu.be/DXdP9U__HN8

This is a video taken in the spring last year that shows parts of our landscaping. I highly recommend engaging a local landscaper who can recommend plantings that are properly conditioned for your local soil and climate. Also, they will properly space them which many homeowners do incorrectly.

As to purchased Pergola being sufficiently strong, it depends on how it is constructed and anchored but those I’ve seen at big box retailers, probably not.