She's continuing the policy of her Green predecessor. Who was continuing a policy drawn up around the turn of the millennium by Fraunhofer: Balance renewables with gas peaker plants which then at one point can be weaned off fossil gas and switched over to synthetic gas. There's other forms of grid storage, but Germany can store three months worth of total (!) energy consumption in its pipeline network so it's ideal for long term, seasonal, storage.

Also see the deals Germany made with Namibia and Canada to supply green hydrogen (in the form of ammonia because easier to transport). Much of the German pipeline network is built to a standard that allows it to transport pure hydrogen (it started out as a hydrogen network) and re-declaring some pipes and building new ones is an ongoing process, there's going to be a full separate network before long.

Why not batteries? First off, those were nowhere near ready when Fraunhofer drew up the plan, secondly, they still don't have the same tradeoffs as synthesising fuel: They generally have higher round-trip efficiency, but also lose energy over time. Synthetic fuel is less efficient, but doesn't lose appreciable amounts of energy over time and it's much easier to store large amounts of it so that's what you want for long-term storage.

Not to mention that we'll need synthetic fuel for some applications anyway, e.g. catastrophe relief: You don't want to rely on electric field kitchens when the grid is down. The current ones run on diesel, just as all the vehicles, and you don't want to be in a situation where you can't use that 70yold semi-mothballed Unimog. The reserves are deep and push come to shove, you want to field them.

No, that's a rather conservative estimate. My federal state alone has more than 20GW in total capacities. And the backup for the rare days when neither solar nor wind produce relevant amounts needs to be able to cover the demand.

The actual point is having those power plants yet in the end never using them aside from those few days a year. And then producing the gas for them climate-neutrally with reneawable overproduction from the remaining 98% of the year.

PS: That the positive thing about solar and wind prices nowadays. They are actually so low that other production methods simply can't compete and won't be used more than actually needed.

PPS: That also the actual economic reason why nuclear is a bad idea. You also need enough production capacities for a cold winter night without solar and wind... but then producing less the remaining time of the year doesn't actually save you money because fuel is a miniscule part of nuclear costs. Have you never wondered why the two countries in the EU pushing for a properly scaled green hydrogen market are Germany and France? Because both models only work economically with peak-burners based on greenly produced gas.

Canada has no capacity to liquify natural gas. There's a shared Canada-US natural gas pipeline system, so some molecules one gets may be coming from Canadian extraction, but it'll pass through a US-based liquification plant, so from Germany's standpoint, that'd be where an export would come from, as that's where it'd be loaded onto a ship.

EDIT: Warren Buffett spent years trying to build one Canada-based LNG plant and fighting environmentalists opposed to it in Canada. He eventually threw in the towel.