
hinzukommen
to be added
To be added to something already existing or to occur additionally.
Zu den Materialkosten kommen noch die Arbeitsstunden hinzu.
The working hours are added to the material costs.
to be added / to join
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to be added
To be added to something already existing or to occur additionally.
Zu den Materialkosten kommen noch die Arbeitsstunden hinzu.
The working hours are added to the material costs.

to join
To come to a place where other people already are; to join a group.
Wir saßen schon im Café, als später noch zwei Freunde hinzukamen.
We were already sitting in the café when two more friends joined us later.

added to that is
A fixed expression used to introduce another argument or an additional aspect in a discussion.
Das Hotel ist teuer. Hinzu kommt, dass die Lage sehr ungünstig ist.
The hotel is expensive. Added to that is the fact that the location is very inconvenient.
'Hinzukommen' (to be added / to join) is a separable verb. The prefix 'hinzu' comes at the end in a main clause. In a subordinate clause or infinitive, the verb stays together.
Zum Regen kam auch noch starker Wind hinzu.
Strong wind was also added to the rain.
You can often recognize the meaning from the subject. If a person is the subject, it means 'sich einer Gruppe anschließen' (to join a group). If a thing or an abstract concept is the subject, it means 'zusätzlich auftreten' (to occur additionally).
Später kam noch mein Bruder hinzu.
My brother joined us later.
In the meaning 'hinzugefügt werden' (to be added), the preposition 'zu' is often used to express what something is being added to. The structure is then: 'Zu [etwas] kommt [etwas Neues] hinzu.'
Zu den hohen Mieten kommen nun auch noch steigende Energiekosten hinzu.
Rising energy costs are now also being added to the high rents.
The formulation 'Hinzu kommt, dass ...' is a fixed expression used to introduce another argument. It always introduces a subordinate clause with 'dass', in which the verb comes at the end.
Die Wohnung ist sehr klein. Hinzu kommt, dass sie keine Küche hat.
The apartment is very small. Added to that is the fact that it has no kitchen.
to add
When adding to a list, both hinzufügen and hinzukommen can be used. Hinzufügen describes a person actively adding something, whereas hinzukommen describes the additional item itself becoming part of the list. Use hinzufügen with an agent, and hinzukommen when the new item itself is the focus.

Zu der Liste kommt noch ein wichtiger Punkt hinzu.
One more important point is being added to the list.
Ich füge der Liste noch einen wichtigen Punkt hinzu.
I am adding one more important point to the list.