As mcdouglasx said, you can't. Currently, your option here is to enable logs, and take note of the "as new interface" lines' timestamp indicating the Electrum server (node) that you're currently using at that time. Other connection-related logs are for extra servers that aren't used to broadcast your transactions. Then the tricky part: You must cross-check the transaction in your history and the "adding signature for" log's timestamp indicating when it's signed by the wallet. "Tricky" because it could've been signed and saved locally but broadcasted on a later date, in this case, you should see a log about saving it to wallet.storage next to it. In case it's saved externally (e.g.: psbt) and imported later to broadcast, you can't fully rely on the logs about its txid in the synchronizer since it can also mean that it's broadcasted elsewhere. But since it's personal (you said "I used to broadcast"), you should be able to remember if it's the case. On the other hand, the time in the GUI are based from the confirmation time, not when it's broadcasted so you can't rely on it. Once you get a good indication of its timestamp based from your assessment on the available info, compare that to the last "new interface" line during that session. That should be the first node where you broadcasted the transaction. Of course, if you haven't enabled logging at that time, you can't do this. This can be done by checking which miner mined the particular block where your transaction is included. Using blockexplorers could answer this if the miner (pool) is known.
As mcdouglasx said, you can't. Currently, your option here is to enable logs, and take note of the "as new interface" lines' timestamp indicating the Electrum server (node) that you're currently using at that time. Other connection-related logs are for extra servers that aren't used to broadcast your transactions. Then the tricky part: You must cross-check the transaction in your history and the "adding signature for" log's timestamp indicating when it's signed by the wallet. "Tricky" because it could've been signed and saved locally but broadcasted on a later date, in this case, you should see a log about saving it to wallet.storage next to it. In case it's saved externally (e.g.: psbt) and imported later to broadcast, you can't fully rely on the logs about its txid in the synchronizer since it can also mean that it's broadcasted elsewhere. But since it's personal (you said "I used to broadcast"), you should be able to remember if it's the case. On the other hand, the time in the GUI are based from the confirmation time, not when it's broadcasted so you can't rely on it. Once you get a good indication of its timestamp based from your assessment on the available info, compare that to the last "new interface" line during that session. That should be the first node where you broadcasted the transaction. Of course, if you haven't enabled logging at that time, you can't do this. This can be done by checking which miner mined the particular block where your transaction is included. Using blockexplorers could answer this if the miner (pool) is known.

As mcdouglasx said, you can't. Currently, your option here is to enable logs, and take note of the "as new interface" lines' timestamp indicating the Electrum server (node) that you're currently using at that time. Other connection-related logs are for extra servers that aren't used to broadcast your transactions. Then the tricky part: You must cross-check the transaction in your history and the "adding signature for" log's timestamp indicating when it's signed by the wallet. "Tricky" because it could've been signed and saved locally but broadcasted on a later date, in this case, you should see a log about saving it to wallet.storage next to it. In case it's saved externally (e.g.: psbt) and imported later to broadcast, you can't fully rely on the logs about its txid in the synchronizer since it can also mean that it's broadcasted elsewhere. But since it's personal (you said "I used to broadcast"), you should be able to remember if it's the case. On the other hand, the time in the GUI are based from the confirmation time, not when it's broadcasted so you can't rely on it. Once you get a good indication of its timestamp based from your assessment on the available info, compare that to the last "new interface" line during that session. That should be the first node where you broadcasted the transaction. Of course, if you haven't enabled logging at that time, you can't do this. This can be done by checking which miner mined the particular block where your transaction is included. Using blockexplorers could answer this if the miner (pool) is known.

As mcdouglasx said, you can't. Currently, your option here is to enable logs, and take note of the "as new interface" lines' timestamp indicating the Electrum server (node) that you're currently using at that time. Other connection-related logs are for extra servers that aren't used to broadcast your transactions. Then the tricky part: You must cross-check the transaction in your history and the "adding signature for" log's timestamp indicating when it's signed by the wallet. "Tricky" because it could've been signed and saved locally but broadcasted on a later date, in this case, you should see a log about saving it to wallet.storage next to it. In case it's saved externally (e.g.: psbt) and imported later to broadcast, you can't fully rely on the logs about its txid in the synchronizer since it can also mean that it's broadcasted elsewhere. But since it's personal (you said "I used to broadcast"), you should be able to remember if it's the case. On the other hand, the time in the GUI are based from the confirmation time, not when it's broadcasted so you can't rely on it. Once you get a good indication of its timestamp based from your assessment on the available info, compare that to the last "new interface" line during that session. That should be the first node where you broadcasted the transaction. Of course, if you haven't enabled logging at that time, you can't do this. This can be done by checking which miner mined the particular block where your transaction is included. Using blockexplorers could answer this if the miner (pool) is known.