BRUSSELS—The European Commission on Thursday proposed extending looser state aid rules for virus-hit companies for six months to June 2022 in a bid to slowly wean them off the billions of euros provided by governments across the European Union. The EU executive, tasked with ensuring a level playing field in the 27-country bloc, also proposed two new measures to encourage investment support and solvency support for a limited time to help Europe rebound from the impact of the COVID-19 pandemic. The so-called Temporary Framework, adopted in March last year and due to expire at the end of this year, has allowed EU countries to pump in more than 3 trillion euros to thousands of companies across the bloc. “We need to be aware of disparities across member states and the need to avoid cliff-edge effects when withdrawing public support,” Commission Vice-President Margrethe Vestager said in a statement. “We are therefore …