Revised Cusco focused itinerary for opinions/thoughts

Hi,
Following previous responses and further reflection on how much I want a 'busy' checkbox tour vs deeper experience, I have decided that I will probably focus much more on Cusco/Sacred valley and other hikes. I am keen to hear specifically what I should prioritise within that itinerary/any unique or less well known ideas.

Further context for me - I am relatively fit, but recently did Acatenango and went from totally fine at 3000m to feeling very ill after 3200m until the next morning, so I suspect while I don't tend to struggle at all with 6+ hr hikes, I do handle altitude badly. Have been learning spanish and would love to make use of that (limited vocab but A2/B1 level at present) and/or potentially take a few more 1:1 classes in Cusco, and would really like a mix of culture/history/adventure. Not looking to splurge where I can budget, but not looking to cut out anything genuinely worthwhile either even if it is expensive (e.g. top class stargazing, cheapish flights that save a day or two)

Draft itinerary:
May 5 - fly to Lima
May 6 - walking tour ?food tour in evening vs try to book a world class restaurant if still space
May 7 - Fly to cusco, move down to Ollantaytambo same day for easier altitude adjustment
May 8 - Explore ollantaytambo
May 9 - ?ideas, end at aguas caliente
May 10 - buy tickets for machu pichu in the morning since no other option, unclear what to do May 10 afterwards, likely nothing
May 11 - Machu Pichu, return to cusco
May 12 + 13 - Cusco (ideas?)
May 14 - Humantay lake
May 15 - Relax, ?Spanish class
May 16 - Rainbow mountain
May 17,18,19 - Cusco (ideas?)
May 20 - Fly to La Paz
May 21 - La Paz
May 22 - Fly to uyuni flats
May 23 - 3 day tour to Atacama
May 25 - arrive atacama
May 26 - stargazing tour if possible since will be a new moon
May 27, 28, 29 - Atacama ?day tour trips vs pick multiday tour (ideas welcome)
May 30 - Fly to Santiago
May 31 - Leave Santiago

TLDR:
- Is 13 days cusco plenty to really explore the area and worth the loss of world-class food in Lima or other tickboxes along the coastline
- What do people actually suggest as activities/how intense are these hikes?