Based on our record, Deputy should be more popular than Tweetbot. It has been mentiond 2 times since March 2021. We are tracking product recommendations and mentions on various public social media platforms and blogs. They can help you identify which product is more popular and what people think of it.
A quick search yielded https://wheniwork.com/l/employee-scheduling and https://deputy.com. Not self hosted but seem like they would fit your needs. The latter might cost but I guess you can reach out to them for non-profit discounts perhaps. Source: over 1 year ago
Use deputy.com and switch to all breaks are unpaid. Clock off for any break longer than short toilet break. Source: over 2 years ago
A new one is in development by TapBots, makers of Tweetbot. Source: over 1 year ago
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