Where does a draught come from when the window is shut?
Run a thin strip of paper around the perimeter of the closed window. Distinguish the fixed frame-to-wall joint from the rubber gasket on the moving sash.

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Check which line is leaking air
If air passes between sash and frame, inspect the gasket and see whether the sash sits square. Sealing along that line would glue the window shut. Keep drainage holes and ventilation openings clear.
Before opening the cartridge, try the Presch silicone gun in the tightest corner. Check you can turn your wrist and release pressure at the end of the run.
Dry-fit the FUGENFUX profiling tool. Choose the edge that meets both sides without scooping out the middle, then tool the bead before a skin forms.
Treat the fixed joint separately
A paintable acrylic may suit a dry interior joint if it accommodates the expected movement. If a crack runs around the frame, water gets in or installation foam is exposed outside, investigate the installation before finishing the inside.
For a dry interior joint that will be painted, check the expected movement against the data sheet for OTTOSEAL A205. Try the finish with your actual paint.
Make two passes
Follow the sash first and the frame second. Mark where the paper moves and repeat in windy weather. A draught from a shutter box can be felt at the frame even though the gap is higher up.
If the draught comes from a fixed external junction, check the installation first. Consider OTTOSEAL S110 only for a specified compatible façade seal, never for gluing the sash.
Tools and materials for this job

OTTOSEAL A205
For a dry joint that will be painted. Check movement and paint compatibility.

OTTOSEAL S110
Neutral construction silicone. Check both substrates on the data sheet.

Presch silicone gun
Manual cartridge gun. Check you can release pressure in the last centimetre.

FUGENFUX
Profiling tool. Dry-fit the edge that reaches both sides of the joint.
Should I fill the slot along the bottom of the frame?
Identify its function first. A drainage outlet must stay open even if you feel air nearby.