Yes, some quick searching will show you that quite a few major brands are in the process of either building battery factories, or about to be building battery factories.
Reference for easier searching: Northvolt (new manufacturer) is working on a major factory with VW, CATL is building new factories, daimler is about to have a new factory come online, etc etc.
Yeahbut. The number of trucks on the road is minuscule compared to passenger cars, they just put on a lot more miles. A kilogram of lithium used in a truck battery will accomplish more than a kilogram of lithium used in a car battery. (Which also suggests the industry may be less cost-sensitive and able to tolerate price increases if they ever happen, although the trajectory is solidly downward.)
Furthermore, secondary use of EV packs (when they're down to maybe 60% of nameplate capacity, they're replaced and the old ones are sold into stationary applications) means that there'll be _decreasing_ demand for purpose-built stationary batteries. Five years ago, if you wanted to put together a massive lithium backup system, you had to buy new batteries. Today, you can head over to batteryhookup and get BMW, BYD, Mercedes, and other ex-EV batteries for pennies on the dollar, in modules with the connectors on 'em and everything.
The industry is actively pursuing this, by the way. Five years from now, it'll either be much easier and more official, or wrapped up in-house and out of third-party reach. But either way, the path from EV to stationary use is developing, and the packs which already did some service on the road, will fill much of the need for stationary batteries, displacing that market's appetite for virgin batteries.
As the secondary market floods with ex-EV packs, at some point it becomes economical to "mine" the really-dead ones for their lithium, and the loop closes. Recycling plants aren't the same as virgin-lithium plants, but we'll see those developing in due time.
Yeah, people are harping about how much minerals we need to dig up for all those batteries. Yes, that's true, and we should certainly seek to mine those minerals with minimum environmental damage, and seek out new battery chemistries not needing critical materials (e.g. Tesla has announced their next gen batteries will be cobalt-free).
But as you say, batteries can be recycled into new batteries. At some point we'll approach some saturation point, where most of the need for those minerals can be satisfied by recycling old batteries. As opposed to fossil fuels which just go up the tailpipe, and thus need new resources to be extracted constantly.
Car makers for the most part don't build their own cell factories. They do invest in battery pack factories.
However, there are major supply contracts being signed all the time. The major battery producers, Panasonic, CATL, LG, SK, Samsung SDI and even BYD. GM and LG have a major partnership and are building a factory in Ohio. SK is trying to build a factory in the US as well.
At the same time you have many new players coming onto the market. Tesla themselves are the most relevant. There are also major European projects, such as Northvolt (former Tesla guys from Giga Nevada) but also others like GigaVaasa. Northvolt will also build a large factory in Sweden, and a somewhat smaller one in Germany. CATL is building battery factories in Czech Republic and expanding existing factories.
There represent long term off-take agreements between car manufactures and cell providers.
Pretty much all of these have large contracts and are building factories all over the place.
All that said, nobody is as aggressive as Tesla with their targets. In fact, a good argument can be made that everybody else is copying the Tesla Gigafactory as a model. Even calling them Gigafactories and targeting the same sort of output levels.
In terms of car makers Tesla (and BYD) are the ones vertically integrating the battery.
Tesla are literally building enormous factories around the world. Are other brands?