is this the new formula?

I don't know as I don't buy these products (was looking to see if this one was worth buying-nope- But I wanted to correct that this is NOT 'chemical free' as most people understand that term to mean. If you read the ingredients it clearly contains unnatural, processed ingredients. Don't be fooled by 'plant based', If you want 'chemical free' you're looking for something like Castile soap.

Is this a “no scrub” formula like the Medela soap?

I use it on all of my babies items, bottles, spoons, cups, plates etc... never have to scrub highly recommend

You would have to research all the ingredients, but if you want non toxic go for pure unscented Castile soap. I say unscented because some use essential oils for fragrance which may be harmful if accidentally ingested. If you aren't worried about that though find a brand like Dr. Bronner's and pick any scent you like. Also be aware Castile soap will burn if it gets in eyes because it does not have numbing agents/chemicals in it. Another option would be African Black Soap. With anything though you have to read and research ingredients in every item/brand you look at to make sure it's up to your standards. Frankly, I have looked at other Babyganics products (like sunscreen) and it appears to be a greenwashed brand. I would not use it due to not containing natural and/or organic ingredients.

Where can I find na again a expiration date

There is a printed batch number on each bottle, contact babyganics through their website's contact form and provide the number to get the manufacture date and expiration date. A little difficult but soap typically expires 3yrs from manufacture of it contains moisturizing and essential oils. I would provide them with a batch number and find out.