Potted plants are often bought to sell a house as the sellers know they can bring them with them. Vines in pots can be put in that look like they have been there for years but they have just been placed with trellace included.
You would need to specify as people have mentioned if you want them. If somebody has nurtured a plant for 10 years they might not want to give it away.
The golden rule which your solicitor can/ should ensure is that the garden and its contents are yours on the day of signing and/ or agreeing - so take photos - as this is the house you are buying not a varied version. If the plants are in pots inside or out - and you want them then like indoor or outdoor furniture you'll need to negotiate, soilcitor will do this for you.
A house will cost hundreds of thousands of € while a few potted plants will most likely cost a few hundred € at most. Don't lose focus on the big picture here!