Anyone there?

If you have given a written, dated and signed notice, it doesn't really matter whether they acknowledge it or not? You have done your part.

Indeed, although I would add to send it by a means that they cannot refute they have received it, so signed-for delivery or read-receipt on an email.

Follow-up email?

you did your part. when you are done, don't show up, period. they don't have a choice.

You don't need their permission to quit. Keep the receipts and walk out. Why do people think they need permission to quit a job?

Keep all the evidence you have regarding your notice. Emails, texts.. Everything! As long as you have that, it doesn't matter. They don't have a say in whetever or not your notice is valid, especially after a year. Go to your new job.
If your old workplace causes you trouble because of the notice, sue them; they had a year to answer.

but like just walk out, if you're done wasting your time with them, just move on. if the roles were reversed they'd drop you in one 5min talk without any forms of notice, don't be afraid to do the same

You gave your notice, I would just go to my new job.

What's the worst they can do, fire you?