When i siphon water some patches can be dirty but often is reasonably clean.
That's a good sign. Using a powerhead in your hand to blast detritus off the rocks and out of the sand is another strategy that can be faster if there isn't a ton to be removed. (Siphoning is better if there's a lot.)
I went away for 4 weeks without water changes, no increase in nitrate. Hana readings are almost none so likely a false reading as it’s being consumed by algae.
I’ve also tried increasing feeding but nitrates don’t increase.
I’d get more corals going to try outcompete algae but worried they won’t survive or will be starved
There's no such thing as a false reading...unless your test kit is broken or you're doing the test wrong.
Reading zeroes means there are no nutrients detectable in the water. This is important (not false).
The reason nutrients are important isn't to lower them and kill the algae (which doesn't work anyway), it's to make sure nutrients
are present enough to *grow everything else*.
So whether algae are using the nutrients up or the nutrients are being teleported out of the tank by aliens is secondary – the test result is accurate and actionable. ;)
However, you aren't growing an algae farm, so removing the algae is the next most important point. You'll see how much dissolved nutrients there are when the algae are gone.
If the algae has grown out (ie you can see it, it waves in the water, etc) then it's too grown for your cleanup crew so YOU have to remove it by hand now. (Use a technique like I described if there's a lot of algae.)
Adding corals will be an excellent third step, but wait until you've cleared out most of the algae (at least) before adding any.
(BTW, if you already had corals the short term plan would include dosing NO3 and PO4 to stop any damage being done to them.)