You certainly want to make your website investment sustainable. In doing so, it's important to consider the following cost factors.
Whatever the case, you have to plan for certain monthly hosting costs as your website must, of course, be accessible to users. Depending on performance and security measures such as automatic backups, you can expect monthly costs from 20 euros upwards for serious high-quality hosting.
It may be that your website is managed by an open-source editorial system such as WordPress. At first glance, this appears to be free of charge - read more about this in the Maintenance section below. However, if your internet agency opts to use a proprietary software-as-a-service system, you will pay a monthly fee (sometimes hidden in the hosting) that is invested in the further development and security of the system. The best-known representatives are the construction kits from 1&1, Strato or Wix. However, there are also high-quality solutions such as Webflow, which are primarily aimed at professional agencies.
Especially for open-source editorial systems like WordPress, it is highly recommended to conclude a maintenance contract with your agency. Here you can calculate with costs from 100 euros per month, which flow into updates, maintenance and care of your system. This prevents outdated plugins from giving up their function or unauthorised persons from gaining access to your server. The latter, by the way, is the responsibility of the site operator.
For larger projects, there may be additional running costs such as the operation of a staging environment, a content delivery network (CDN) or other services. These can vary greatly and would go beyond the scope of what is reasonable here.