Your TV is too old. According to this
Best Buy page of reviews for the Sony KDL-52W3000 BRAVIA, it was built before 2013. The latest reviews are 2008. An
Amazon search yields the same last year of reviews. All the
current apps and devices that would need to upload or be installed or attached to a smart TV are made and configured for TVs made
2013 and beyond.
I know this because I share your frustration. I have a "smart TV" made in the middle of 2012. It was the 1st generation of "smart TVs." So I thought I was buying the latest technology and would be able to add on from that. I also have 3 HDMI ports AND a USB port, and some "smart TV" button which switches to a page of smart TV features like Hulu,
YouTube, some other streaming services. Ha!
I use my HDMI cable all the time. Love it for that. I hook my tablet or PC to it all the time. I run any stuff I want streamed or shown on the TV
on my
tablet or computer and mirror it to the TV through my HDMI cable. Same as what you are doing.
That unfortunately is the extent of what I can do. PERIOD.
I have a Samsung. It has a native Samsung app pre-installed in the TV to cast from devices to my TV. Unfortunately, because this "smart TV" was made before 2013, there is NO software, no app that can be downloaded that will either
update or replace any of the streaming services already on the TV. Nothing NEW can be downloaded, added, installed as the hardware equipment in the TV is half a year too old to be recognized or can run it. Samsung stopped using the casting app, and 2nd generation replacement casting app. They now have something totally different that won't work with my TV.
All OTHER casting apps/mirroring apps that I've tried do not work with this TV. I've tried, with the MANY generations of cellphones I have.
Same for ALL the pre-installed streaming services. None will install any updates. I CAN hook up my TV to the Internet. But, that doesn't do me any good when all Internet technology basically needs everything post-2013 to work with my TV.
Your TV doesn't even have a USB port, I think? I don't see one listed under
your TV's specs.
Mine does have a USB port. I MAY be able to
plug in a Chromecast dongle to it. Or other dongles, sticks, etc. But, again, since the TV's pre-2013, it's unlikely that any software in any dongle will work with my TV to wirelessly connect it to my computer or tablet. There is NO software in the TV that will recognize the software in the dongle. And no way to download, install or update any thing on the TV. So, I will have just wasted $65 on a dongle.
The only thing that runs via the USB port is an older wireless keyboard.
The HDMI port no longer works on my tablet. So I can no longer connect it to my TV. The
only 10-inch tablet on Amazon that even has an HDMI port is one for $129 and is not a brand I want.
OR. . . I can simply add on another $125-ish and get a new 2020 smart-TV that immediately work with every device I have and do everything I need a smart TV to do.