This is a very useful guide from Young Minds youngminds.org.uk/find-help/for-parents/parents-guide-to-support-a-z/parents-guide-to-support-school-anxiety-and-refusal/
School should be working with you to address your child's anxiety around school, ask them for support through the pastoral team or the Education Welfare Officer if they have one based in school.
School is not required to provide work after 15 days, that applies to exclusions not to Emotionally Based School Non-attendance. Providing work to be done at home without having devised a return to school plan with you and your child is likely to increase anxiety rather than reduce it. Tuition at home is based on medical need and anxiety is not covered under this without another health condition that cannot be managed in school or would significantly disrupt learning.
Please contact school to request support with a return to school plan if that is what you want to happen. I'm surprised they haven't been in touch already but it's still early in a hideous term so they have perhaps not caught up yet.
A good return to school plan should be child centred and can incorporate strategies to encourage a child into a school environment, eg a reduced timetable that gradually increases. It could start with short school visits to reorientate your child or even something as simple as getting up at "school time" and putting on school uniform. It needs to build gradually and will occasionally push a child out of their comfort zone but not at a pace that causes the whole plan to crumble.
If your school is offering blended learning for children who are isolating at home you could tap into that as part of the RTS plan but this isn't going to be sustainable long term.
Your other option, as you know, is EHE, and it's a straightforward process to deregister your child, as described above. You should have an Independent Advisory Service locally, if you google your local authority and IASS you should find them.
Good luck and I hope all goes well for you both.