That's the CAP part. The annual co2 emissions of electricity production and industries is capped to X gigatons per year. If a datacenter buys all clean electric production of the country, electric companies will have to either have to make up the gap by building more new clean energy or tell other customers "sorry all sold out".
Of course, would the latter happen, political actions would be done before people freeze. It will be unpredictable what the would be - allow fossil fuels "temporarily" or order datacenters to shut down during dunkelflaute? Interesting times (I would prefer less interesting times).
Generally speaking cap and trade is the most sure way to reduce emissions (emissions drop exactly at the pace the CAP drop annually) and the most cost-effective way also - the TRADE part ensures emissions are cut first by those who it easiest, while hard-to-decarbonize sectors have most time to sort their plan.
The only problem is "carbon leakage" where co2 emissions simply move to asshole countries like USA and China that do not utilize cap-and-trade. That should be dealt with hefty carbon tariffs. Oh wait, even china is building their own cap-and-trade system. Well, anyways, tariffs against the climate assholes.
The EU has a large problem with carbon leakage from electricity generation to oil and gas use.
For example, gas heating is exempt from the EU carbon trade, so people are encouraged to use that rather than electric heating. In countries like Germany, gas heating is popular largely for tax reasons.