I don't think you need to follow a set routine: stretching & mobility is very personal, and should be in response to
a) what you do for the rest of your day
b) what your goals are
So my mobilising before a gym session in the morning when I know I'm going to lift heavy weights is different from my mobilisation before a 90 minute ballet class in the evening.
And my stretching after each of those sessions is different.
Focus on mobility rather than stretching or flexibility: stretching works by breaking tiny tiny muscle fibres under full range of motion / stress and the idea is that as they heal, your muscle lengthens.
Mobility is what you need to start with: a focus on getting the large muscle groups moving. You should always do a literal warm up - raise your body temperature - first. 5 minutes of walking vigorously or very gentle running (on the spot if necessary) or maybe 20 burpees.
Then think about mobilising the torso - forward roll of the spine (keep the knees soft or bent), sideways twists each way, sideways bends to reach your hand down your thigh/to the side of your knee.
Then think about your shoulders - shoulder rolls and arm swings.
Ditto legs - leg swings - forwards, backwards, sideways.
Circle your hips each way. Raise your knees to your chest.
Rotate your ankles, and think about "doming" your feet to work your insteps & arches (look on YouTube for demonstrations of doming - ballet dancers do it to gain strength in their feet.
Work up or down your body, mobilising each part.
Seated stuff can include deep static lunges, and the 90 degree "knee box" mobilisation for your hips - again, search YouTube for demonstrations.
Go by how your body feels - I always need to do the yoga Plough, and mobilise my hips in various ways as I spend about 10 hours a day at my desk.