Let's try to simplify this.
You wil need to know a few things about your device, because the app that you desire may come in different versions for different devices.
You will need to know the Api number and the OS version.
Typically, these are are found by {your device may vary}:
Settings
System
About phone
Your new phone has a browser.
Use this browser to access an appstore with the capability to download previous versions of apps. {Not the Play Store}
There are a few well trusted ones out there.
https://www.apkmirror.com/
https://m.apkpure.com/
https://en.uptodown.com/
{These are a few of what I use- I did not check to see if your app was on them. If it is not, then use the browser on the device to access the same site that you did with your PC.}
Find the app, locate the version that suits your wants and device, and use the browser to download it.
If your browser is incapable of doing this, or else it is difficut , then you need a different browser.
Most {ie., all} stock browsers are sheer garbage, and Chrome is not really any better for other {and the same} reasons.
Let me know if you need a browser that makes this sort of thing extremely simple.
Once the apk of the ap is downloaded, you can find it in your file manager and LONGPRESS it.
A menu with options should appear, with INSTALL being the one you want.
Once again, if it is not just this simple, then I would recommend another file manager- for the same reasons as with the browser.
If INSTALL comes up, and you select it, a screen designed to scare you will appear, telling you that you cannot install from such sources unless you opt to 'Allow Untrusted Sources' or whatever.
Yes, this notice sounds scary.
Disregard it, as you can always go back and change it after you get this app installed, if you choose.
Now, if you longpress the apk in your file manager, and install is not an option, then the most simple thing to do is to download and install an apk installer app.
The one that I use handles a variety of types of apks and is most efficient.
Once again, be prepared for that 'scary message' here, as well.
Ok, so I just checked, and although I got nothing when I typed SendLeap into the search areas in the appstores that I listed, I did a general search {DuckDuckGo} with my phone, btw, and got the link from APKPure, one of the sites listed above.
https://m.apkpure.com/sendleap-text-from-your-computer/com.moduloapps.textto
The apk installer that I use is from the same appstore:
https://m.apkpure.com/xapk-installer/com.apkpure.installer
Sorry for the rambling post, lol.
At any rate, the point here is to never think that Google is your only resource for apps.
In fact, at this point, they are my last source.