Via the council's active travel team:
"From 12th October, for 25 weeks, Spylaw Car Park will be closed Monday to Fridays.
On Thursday 15th October the Water of Leith Walkway/National Cycle Network Route 75 will be closed downstream of Colinton Tunnel. Unfortunately we are not able to sign post a suitable diversion and would ask people to plan ahead and use an alternative route.
Closures are in place on the Water of Leith Walkway/National Cycle Network Route 75 at Baberton Loan, Juniper Green. Diversions must be followed and we ask all users to be courteous and responsible."
If I'm reading it right, it's only the car park that'll be closed for six months - the walkway itself will only be closed on the 15th, but at least part of it will be a "temporary footpath" when it is open, which may or may not be particularly suitable for cycling.
More information here: https://www.scottishwater.co.uk/in-your-area/investments-in-your-area/water-of-leith/kingsknowe-cso