The HSE is going to offer €750 to each claimant, plus a contribution of €650 towards their legal costs. Presumably anyone who can actually point to a concrete loss or harm that they suffered as a result of the data breach will not accept that — they'll hold out for compensation commensurate with the harm they have suffered. So this looks like an attempt to clean out opportunistic or nuisance claims at relatively little cost. (It will, of course, only work to the extent that people accept the offer.)
Will it lead to a flood of new claims? I suspect not. The HSE is under no obligation to make the same offer to everyone who brings a claim. Anyone who hasn't claimed up to now, but now makes a claim. does look like a chancer and the HSE may well decide to make them no offer at all, at least intitially, and simply wait to see how far they push their claims.
Lawyers who work on a no-foal no-fee basis are not going to be interested in acting for clients who want to lodge a claim in the hope of getting an offer of €750 + €650 — there's a more than sporting chance that the offer will not be made to new claimants, and even if it is the fee the lawyer might hope to get (€650 plus some slice of the €750) would be small. Between those two factors I don't think the business will be hugely attrractive to lawyers who work on contingency fees. So I think anyone wanting to lodge a claim is either going to have to pay lawyers to act for them (with no guarantee of getting even an offer of €750) or is going to have to proceed without a lawyer — which you can do, but it takes a fair amount of time and energy for a very uncertain return.
More than 90,000 people were affected by the breach; only between 600 and 700 have made a claim, which means that the vast majority of people don't think they have suffered any harm, or at any rate they don't think they have suffered any harm that could be meaningfully compensated for with money. I don't think many will be encouraged to lay out good money now for the somewhat uncertain chance of someday getting an offer of €750.