Have you got access to the top?
In other words, is the loft up there?
If so, stick a piece of wood above with adhesive and when dry use wood filler to close the hole and once that is dry, normal filler to reproduce the ceiling texture.
If not, a few options: a touch of expanding foam and then filler or gripfill in stages to close the hole, then filler.
Short length of wood or plasterboard offcut with a screw in middle.
Blob of no more nails on each end.
Put into hole so bridges both sides and pull down with screw to make no more nails stick.
Remove screw and once dry cover with filler.
Sfk
That timber is probably the supporting joist rather than a backing board.
To the OP. Try to chamfer the hole backwards at the back edge. Cut a circle of card, (big enough to overlap the hole by about 10mm all round), with a small hole in the centre to push a piece of cotton/thin string through and tie the string to a matchstick. Gently bend, (without creasing), the card and feed it through the hole. Roughly centre the hanging thread and gently pull till the card is laying flat across the hole. Gently fill the hole with your chosen filler making sure you fill in the chamfered back edge. It may take a couple of layers of filler depending on how thick the ceiling is. Once filled and the filler has set cut the thread as close at possible to the ceiling and finish with a fine layer of filler. Once set you can match the surface to your existing pattern and paint.
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