If you cancelled your own plan, you don't get immediate access to an Apple Music Family plan that is still in the free trial portion.
What I asked was if the Apple Music Family Plan was still under the Free Trial, in other words, the Family plan was recently subscribed to by the Family Organizer and has not yet charged them the first time.
In that case, once the Family Plan renews into a paid subscription and charges the Family Organizer you should get access normally.
Manually canceling your own is what caused the delay. Otherwise the transition is automatic and seamless as Apple automatically cancels your plan when you join a family group with a shared Apple music subscription plan.
Do not renew your own plan, there's no point at this time to do that. Just wait until the Apple Music Family Subscription renews from the Free Trial into a paid one.