chore: propagate context across all layers

[rmanibus]

This PR fixes context propagation issues in the engine and client layers, which were using context.Background() instead of the provided context. This ensures that cancellation and timeouts are respected throughout the codebase.

[codecov]

Codecov Report

❌ Patch coverage is 59.76331% with 68 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
cmd/cloudstic/cmd_profile.go	30.43%	16 Missing ⚠️
cmd/cloudstic/cmd_store.go	70.96%	9 Missing ⚠️
cmd/cloudstic/cmd_auth.go	46.66%	8 Missing ⚠️
cmd/cloudstic/cmd_key.go	0.00%	8 Missing ⚠️
cmd/cloudstic/main.go	56.25%	7 Missing ⚠️
cmd/cloudstic/interactive.go	50.00%	3 Missing ⚠️
cmd/cloudstic/cmd_ls.go	0.00%	2 Missing ⚠️
internal/engine/backup.go	50.00%	0 Missing and 2 partials ⚠️
client.go	88.88%	1 Missing ⚠️
cmd/cloudstic/cmd_backup.go	50.00%	0 Missing and 1 partial ⚠️
... and 11 more

📢 Thoughts on this report? Let us know!