Do a search for single din CarPlay stereos with floating screens. I think those will work for you.
Good question to ask your Mazda dealer. Specifically if it is Android or iOS (upgradeable) or just Bluetooth. The reason I suggest the dealer is that there MIGHT be software/hardware upgrades that need installation before your query can be accurately answered. These are things that POSSIBLY are not automatically installed in whatever electronics that was originally installed in your Mazda when it was new. At 16 years, your 2006 is from the time of Pentium computers and car electronics were similarly stone-age.
You get music in your car , WOW
A tablet is basically a smart phone with a larger screen.
There are Sony CD player/tuners that do basically this.
Go to Crutchfield.com and plug in your vehicle year/make/model and check out the available aftermarket receivers. Pretty much all of them will Bluetooth link to your phone for hands-free talking, plus allow updated media sources for music files. Some have touchscreens, like tablets.
According to this
https://www.crutchfield.com/S-BOtXmA0yRwC/vehicles/Mazda-Car-Stereos-and-Speakers.html
your vehicle will support a double DIN unit which supports these features:
🚘 Compatible with Apple Carplay & Android Auto: Just connect with your smart phone that make it possible for you to access map navigation, phone contacts, email, notification, allowing you to make phone calls, navigate, play music with the help of Siri or Google voice assistant. Make you safer from having to look down at your phone while driving.
🚘 Phone Mirror-Link: Support “stereo-phone interconnection” with most cellphones. Through mirror-link, the car stereo will display the content from your cellphone screen synchronously such as maps, movies, games.
🚘 Bluetooth 4.2 & Enhanced Listening Experience: Answer your important phone calls without distracting your attention from the road with our MINYE stereo which features a hands-free bluetooth system, allowing for easy smartphone pairing ( built-in clear mic)! Wireless audio stream via bluetooth provides a stable connectivity to your smartphone or bluetooth device, MINYE allows you to enjoy a superior music listening experience!
🚘 Reversing Image Function: Equipped with a unique 12 LEDs wick reversing camera, bringing you clearer night vision distance. The 7-inch touchscreen will automatically display the reverse image once you put the car into reverse gear. Make your daily reversing safer.
🚘 Upgraded Full Touch Screen: Compared with resistive screen on other stereos, MINYE capacitive screen solution has higher sensitivity and accuracy. Meanwhile, the traditional physical buttons are cancelled and the full touch solution comes on stage. It greatly enhances the human-computer interaction experience. You can now feel the silky smooth operation feel on the car screen! The professionally tuned 1024*600 HD LCD screen bringing you an excellent visual experience.
🚘 How to choose the correct stereo for your car: This stereo is universal double din standard. The only suggestion is to check whether the original installation slot of your car matches 7.01(L) x 2.36(W) x 4.06(H) inch. Under the correct installation size, there will be no compatibility issues in use. Welcome to contact our 24-hour online customer service if you have any questions about installation and wiring.
A competent car stereo dealer/installer should satisfy your detailed inquiries and meet your requirements.
Our CX3 does that. I had to pair the phone via Blue tooth. Now it happens automatically.