Has Timestream for InfluxDB limit on the number of organization?

There is no explicitly documented limit on the number of organizations you can create within a Timestream for InfluxDB instance. According to the documentation, a DB instance can host multiple organizations and multiple buckets associated with each organization.

The issue you're experiencing where the InfluxUI only shows the first 20 organizations while you have successfully created 24 organizations appears to be a UI pagination limitation rather than a service quota. Since you were able to create 24 organizations without errors, this suggests there isn't a hard limit at 20 organizations.

What is documented is that you are limited to a maximum of 40 Timestream for InfluxDB instances per AWS account by default. This is a limit on the number of DB instances you can create, not on the number of organizations within a single instance.

For the UI display issue, you might want to check if there are pagination controls in the InfluxUI that would allow you to view beyond the first 20 organizations, or consider using the InfluxDB API or CLI to list all your organizations as an alternative to the UI.
Sources
What is Timestream for InfluxDB? - Amazon Timestream
Amazon Timestream endpoints and quotas - AWS General Reference
Amazon Timestream FAQs – Time-Series Database – AWS