const myObjects = {};
Object.keys(data).map((key) => {
    const splitKey = key.split('-');
    const elemId = splitKey[1];
    const realKey = splitKey[0];

    if (!myObjects[ elemId ]) {
        myObjects[ elemId ] = { id: elemId }; // Create entry
    }
    myObjects[ elemId ][ realKey ] = data[ key ]; 
});
// Turn into array
const myObjectsToArray = Object.values(myObjects);
// Or use the myObjects as a key/value store with ID as index
const selectedElement = myObjects[ myID ];

const data = {
  "education_center-266": "Software House x",
  "education_center-267": "Learning Academy xyz",
  "end_date-266": "2022-01-26",
  "end_date-267": "2021-01-22",
  "start_date-266": "2021-01-26",
  "start_date-267": "1998-11-26",
  "title-266": "Web Developer",
  "title-267": "Teacher"
};

const results = [];

function splitKey(key) {
  const indexOfDelimiter = key.lastIndexOf("-");

  return {
    id: key.substring(indexOfDelimiter + 1),
    key: key.substring(0, indexOfDelimiter)
  };
}

function getItemFromResults(id) {
  return results.find((r) => r.id === id);
}

function processKeyValuePair(id, key, value) {
  const item = getItemFromResults(id);

  if (!item) {
    results.push({ id, [key]: value });
    return;
  }

  item[key] = value;
}

for (const k in data) {
  const { id, key } = splitKey(k);
  const value = data[k];

  processKeyValuePair(id, key, value);
}

Here a slightly different solution, first getting all unique id's, then builiding the result array with looping over Object.entries.

let data = { "education_center-266": "Software House x", "education_center-267": "Learning Academy xyz", "end_date-266": "2022-01-26", "end_date-267": "2021-01-22", "start_date-266": "2021-01-26", "start_date-267": "1998-11-26", "title-266": "Web Developer", "title-267": "Teacher", }

const ids= [...new Set(Object.keys(data).map((el)=>{
    return el.split('-')[1]
}))];

console.log(ids) //unique id's

let result = [];

ids.forEach((i)=>{
    let obj={id: i}
    Object.entries(data).forEach((el)=>{
        if(el[0].includes(i)) obj[el[0].split('-')[0]]=el[1];
    })
    result.push(obj)
})


console.log(result);