How to create a new array of objects from two arrays based on object values?

The approach I'd take is to convert your received and sent messages into a single array of "interactions" that contain only the information you care about. For a received message you want to look at the senderId, whereas for a sent message you want to look at the receiverId (the idea is that you want the other user for each interaction, not the current user). That could look like this:

interface Interaction {
  user: string
  messageId: string
  timestamp: number
}

function latestInteractions(
  receivedMsgs: MsgSlice[], 
  sentMsgs: MsgSlice[]
): Interaction[] {

  const allInteractions: Interaction[] = [];
  for (const m of receivedMsgs) {
    const sender = m.messageDataSlice.senderId;
    if (sender === undefined) continue;
    allInteractions.push({
      user: sender,
      messageId: m.messageId,
      timestamp: m.messageDataSlice.timestamp
    });
  }
  for (const m of sentMsgs) {
    allInteractions.push({
      user: m.messageDataSlice.receiverId,
      messageId: m.messageId,
      timestamp: m.messageDataSlice.timestamp
    });
  }

Note that if somehow a received message doesn't have a senderId then we just skip it. Maybe we should throw an error instead? That's up to you. Now we have a single array filled with all interactions. We want to collect just one such interaction for each user in the array, and if we ever have more than one we should keep just the one with the greatest timestamp. That could look like this:

  const interactionMap: { [k: string]: Interaction } = {};
  for (const i of allInteractions) {
    if (!(i.user in interactionMap) || interactionMap[i.user].timestamp < i.timestamp) {
      interactionMap[i.user] = i;
    }
  }

The interactionMap is now a plain object whose keys are the user strings and whose values are the latest Interaction for each user. This has all the information we want, but you want an array and not an object. So we can just use the Object.values() method to get an array of the values:

  return Object.values(interactionMap);
}

That's an array in some order; if you care you can sort it according to your needs.

Let's make sure it works with your example:

const latestInteraction = latestInteractions(latestReceivedMsgs, latestSentMsgs);
console.log(latestInteraction);
/* [{
  "user": "userId1",
  "messageId": "messageId2",
  "timestamp": 102
}, {
  "user": "userId2",
  "messageId": "messageId3",
  "timestamp": 103
}, {
  "user": "userId3",
  "messageId": "messageId5",
  "timestamp": 105
}]  */

Looks good!

Playground link to code

You could simply flatten both arrays into one, then sort them per timestamp. Such as:

let msgs: MsgSlice[] = [];
msgs.push(...latestReceivedMsgs);
msgs.push(...latestSentMsgs);

msgs.sort((a, b) => {
    return a.timestamp - b.timestamp ;
});

Perhaps you can join them into a single array and then sort them by their timestamp?

const sortedMsgs = [...latestReceivedMsgs, ...latestSentMsgs]
sortedMsgs.sort((a,b)=>a.messageDataSlice.timestamp-b.messageDataSlice.timestamp)