The Nano 33 IoT can be a BLE peripheral device.
The Nano 33 IoT supports both Bluetooth LE and WiFi but not at the same time. For many applications this is not an issue, but it sounds like you want it at the same time.
Having WiFi and BLE running at the same time is possible with the NINA-W15, but Arduino did not choose this one. Even with these boards WiFi and Bluetooth are not sending signals at the exact same time. They have one radio and use the same frequencies, so there would be interference. Bluetooth LE sends packets with large intervals (compared to the packet length), so the module can send the packets "interleaved". Bluetooth LE uses frequency hopping on top of it, to avoid interference with WifFi channels that might be actively sending, so only a packet here and there is lost.
So, your application could switch between WiFi and BLE. It is not as fast as the NINA-15 and might not work for every use case, but you can investigate hiding the fact for the user. After all, do you need to look at the webpage and your phone at the same time?
If you do, you could always add a module or connect the two Nanos via SPI. Then one can handle BLE and the other WiFi.