Is what I did correct, giving the banknote to the worker in the shop? And if it is not correct, what should I do? And how and where is lost property announced in public places nowadays, taking into account the cost of advertising?

There is no harm in giving a found item (luqata) to the shop owner to announce it, as he is more likely to know its owner. It is permissible to transfer a found item from the finder's possession to another due to necessity. A valuable found item of significant worth must be announced for a full year in public gatherings. It is permissible to give it as charity on behalf of its owner after announcing it. If announcing the found item incurs expenses, the preponderant opinion is that the finder is obligated to cover the announcement expenses if he took the item with the intention of owning it. He is not obligated if he took it with the intention of preserving it for its owner. The announcement of a found item should be done by describing it generally, without mentioning its details or quantity.