I assume the older ones at least are on a contract phone, likely in your name and paid for by you? If so call the phone company and have them put a temporary bar on the phones. Then call a meeting, set out your expectations and a rota and tell them that their phones will not be unblocked until they agree to and start helping out.
When they are all school go into their rooms and remove game controllers and remotes and they only get them back once they have done a set chore.
Have a visual chore board up in the kitchen so everyone knows what is expected from that and on what day.
Mine are aware that I pay for the phones therefore they are my phones that I allow them to use. And that privilege can be removed at anytime.
Mine are also lazy at doing chores and constantly say I will in 5 minutes. I’m flexible and allow them that 5 minutes rest before they start. Like you recognise, we all get overwhelmed sometimes and don’t always respond well to immediate demands being put on us. So I say that’s ok, have 5 minutes chill and then get yours jobs done. After 5 minutes if they are still reluctant distractions like phones are taken until job is completed.
Mine are 13 and 10 and are expected to tidy their rooms, put their own laundry away, set the table, clear up after meals etc.