I think the RUNE token has been ERC20 at first and later switched to BEP2.
I don't know if my tokens are ERC20 or BEP2.
As I bought them recently at Binance they might probably be BEP2.

I have bought Thorchain/RUNE tokens at Binance.
Can I send this tokens to a hardware wallet? I have a Ledger Nano X and a Trezor.

My addresses are starting with number 3.
I entered the beta wallet in January before the Suite was released.

I think there is a misunderstanding according the beta wallet.
The Trezor beta wallet is for Ethereum and ERC 20 tokens only.
My Trezor passphrase protected wallet is a BTC wallet.
I didn't enter the beta wallet to access my passphrase protected wallet.
I entered the beta wallet just to get to know it.
Why is that worth mentioning?
The passphrase protected wallet worked fine before I visited the beta wallet. The issue occurred after I visited the beta wallet. Maybe that's a coincidence. Maybe there is a connection.
DireWolfM14 quotes the Trezor website: "Closed Beta is designated for experimental testing and access is limited exclusively to the Beta Testers Community." This might be an interesting hint.
I didn't see that message when I entered the beta wallet in January.

I'm sorry I didn't describe the issue very well.
Please find enclosed some additional information:

Hardware Wallet: Trezor One
Wallet names:
- Trezor wallet (for BTC) https://wallet.trezor.io
- Trezor beta wallet (for ETH) https://beta-wallet.trezor.io/next/#/
Description of Problem: sent BTC funds are not shown in recipient wallet
Related Addresses:
- frist transaction: 371HaxAKjJaEMtWLxm1UEpFnH8C2ehuFj2
- second transaction: 32GS4agqd6gzysdjxeVdJucuWhzVc88Xzp
Related Transaction IDs:
- first transaction: 599216c0d80b75f82ee87967c08271426f1a3d4e00c435958b44a4073dadb4c8
- second transaction: d08e36020a08872b3aec8fe0f2551b28c7ac4252dfb8f71d2baa9a5e3bbf4c90

The complete history of the process:
- transferred 0.0495 BTC from the default wallet into one hidden behind a passphrase (first transaction)
- entered the hidden wallet, balance showed 0.04595 BTC received
- transferred 0.04327862 BTC from default wallet into hidden wallet (second transaction)
- entered the hidden wallet, balance showed 0.04595 BTC received and 0.04327862 BTC received
- entered Trezor beta wallet
- entered the hidden wallet, balance shows 0.0 BTC, "no transactions yet", no used receive addresses

The assumptions of HCP are exactly correct. His formulation is better than mine (sorry again)!

@ Coolcryptovator
I bought the device directly from Trezor.
I have a 24 word back-up seed, which I didn't enter anywhere yet.
The passphrase is on top of the seed to create a hidden wallet. To enter the hidden wallet you have to enter the PIN and the passphrase, which worked well at the beginning.

@ o_e_l_e_o
I have entered my passphrase protected wallet and looked for the addresses I sent my coins to.
The addresses are not there.
You are right, that suggests I'm not in the correct wallet.
I don't know how that comes about, because I'm sure I have entered the correct passphrase. (That's why I gave the hint, that my passphrase is short and easy to remember.)

@ Charles-Tim
The Electrum wallet is probably better than the Trezor wallets.
I have contacted the Trezor support. I want to await their response first. After that I will try the Electrum wallet as you described it.

I've transferred BTC from my seed-only hardware wallet into my passphrase protected hardware wallet with the same provider.
The transaction has been included into the blockchain.
I successfully entered the passphrase protected wallet and checked the received funds.
A few days later I entered the wallet again and couldn't find my funds anymore.
It says "0.00 BTC, no transactions yet."
I'm sure I'm using the correct passphrase as it is short and easy to remember.
In the meantime I have logged into the beta version of the Ethereum wallet with the same provider. I've been prompted repeatedly to disconnect an reconnect the device. Might the beta wallet have caused the issue?