"Dust" refers to UTXOs whose cost of spending is a significant portion of their total value. In Bitcoin Core's source code, "dust" specifically refers to UTXOs that are smaller than three times their fee at
minTxRelayFeeRate. For a Pay to Public Key Hash (P2PKH) output, this is 546 satoshi because an output has 34 bytes and an input has 148 bytes. It's a bit smaller for single-sig segwit outputs.
Given that, an increase of the Bitcoin exchange rate would not directly change the definition of dust, but dust amounts would correspond to a larger amount of purchasing power. On the other hand, the cost of spending such a small UTXO would also be significantly higher, making such payments similarly uneconomic as before, just at higher value.
If the price actually goes up by multiple magnitudes (like the 4,000× you suggest), we may see the
minRelayTxFee get reduced by one or two magnitudes. Very unlikely we could even see a hardfork that increases the precision of the amounts on the network to a fraction of satoshis. More likely, the transaction fees on the base layer will be prohibitive for all but the largest payments and smaller payments will live on other layers or sidechains.
Transaction fees in Bitcoin are paid per their blockweight and not per value transacted. This means that on-chain transactions generally don't lend themselves to micropayments since smaller payments have a high relative cost. Micropayments will almost inevitably get pushed out of the blockchain layer to either systems like the Lightning Network, where fees scale with the payment's value, or to off-chain payment systems, where they might be essentially free.