THIM, aka 'Thai Immigration Bureau' was released on June 6th by the Thai government. Here's the iOS version of the app, and here's the Android version. Both are definitely official/legitimate but currently have somewhat low rankings on both app stores.
Does it currently work well? Is it safe to use?
(Note that both the question and the app listings have been modified since this question was originally asked. Originally there were a few things that looked suspicious, including the company name it was listed under on the Play store, but these have been updated, so this answer is based on the current state.)
At this time, the THIM app appears to be completely legitimate, safe, and functional.
The entry on the Google Play Store lists the developer as the "ROYAL THAI POLICE", which is the government department responsible for immigration controls in Thailand. Google Play does verify developer accounts, so this information can be trusted. The support email address for the app is in the domain di.co.th, which belongs to 'Digital Identity', the company that was contracted by the Thai Government to create this app. There are countless other references to this app being created by Digital Identity, such as this press release from Amazon AWS regarding the app.
Many of the concerns around this app seem to stem from the fact that people have claimed it does not work and does not actually create a "Thailand Digital Arrival Card" (TDAC). I can personally confirm that the app DOES work and DOES create a valid TDAC. I used the app yesterday to submit my TDAC. In doing so, the application sent me multiple digitally-signed emails from the domain "thim.immigration.go.th". This is the correct domain for the Thailand Immigration department, and as these emails were digitally signed, they clearly came from a legitimate source.
After submitting my TDAC and receiving the relevant QR code via both the app and (digitally signed) email, I had no issues passing through Thai immigration — which would not have been the case if my TDAC had not been submitted successfully.
One of the other concerns around the legitimacy of this app is that it "doesn't do anything else" other than TDAC — today this appears to be correct. The government has stated that the app will be expanded over time, and there are several "Coming Soon" features in the app itself, but today the only purpose seems to be to submit a TDAC.
Based on (unsubstantiated) claims that this app is sending data to untrusted parties, I decided to confirm exactly where it was sending information by monitoring network traffic when using it. During a full creation/submission of data, the app only communicated with hosts in 2 domains — service.thim.immigration.go.th and ingest.us.sentry.io.
The first of these is clearly under the control of the Thai government and is in the same domain as the website for TDAC submissions. The second is a well-known and trusted application monitoring product, used by countless thousands of apps. Fairly clearly, based on this communication, data entered is not being sent to third parties as has been claimed.