Make a backup first! And test first in develop environment.
To convert all prices from net (german: netto) to gross (german: brutto) ones, you need to issue the following SQL statement.
But at first you need to obtain your attribute_id of the price
attribute. To do so, go to backend > stores > attributes > product and click on the price
attribute.
Obtain the id from the URL (see screenshot below):

In this case it is 67
but yours can be different!
Update catalog_product_entity_decimal set value = ROUND(value*1.19, 2) WHERE attribute_id = #your_attribute_id#
where #your_attribute_id#
would be your previously obtained attribute_id of the price
attribute (in this case 67
).
This query will also round your prices! F.e. if your net price was 19.3193
the result will be 22.99
.
If you have special prices on some of your products, you do need to repeat the above steps for the attribute_id corresponding to the attribute special_price
.
Do not forget to set your catalog prices to including tax
. Afterwards reindex prices via cli php bin/magento indexer:reindex
.