I can't speak for the NestJS vs ExpressJS discussion, but I can given a viewpoint on databases.
The main thing to consider around database choice, is what "shape" the data will be in, and the kind of read/write patterns you expect of that data. The blog example shows up so much for DBMS like MongoDB, because it showcases what NoSQL / document storage is very scalable and performant in: mostly isolated documents with a few views / ways to order them and filter them. In your case, I can imagine a number of "relations" already, which suggest a more traditional SQL solution would work well: You have restaurants, they have maybe a few menus (regular, gluten-free etc), with menu items in, which have different prices over time (25% discount on christmas food just after christmas, 50% off pizzas on wednesdays). Then there's a whole different set of "relations" for people ordering, like showing them past orders, which need to refer to the restaurant etc, and credit card transaction information for refunds etc. That to me suggests PostgreSQL, which will scale quite well if you database design is okay.
PostgreSQL also offers you some extensions, which are just amazing for your use-case. https://postgis.net/ for example will let you query for restaurants based on location, without the big cost that comes from constantly using something like Google Maps API to work out which restaurants are near to someone ordering. Partitioning and window functions will be great for your own use internally too, like answering questions of "What types of takeways perform the best for us, Italian, Mexican?" or in combination with PostGIS, answering questions like "What kind of takeways do we need to market to, to improve our selection?".
While these things can all be implemented in MongoDB, you tend to lose some of the convenience of ACID or have to deal with things like eventual consistency, which requires more thinking on the part of your engineers. PostgreSQL offers decent (if more complex) scalablity and redundancy solutions, and is honestly very well proven and plenty of documentation exists on optimising queries.