Some people care about PE. Some people don’t. It’s just one metric that represents past performance. If it’s high, the market believes the stock price will go up.
No, P/E being high means the stock market thinks the company's income will grow by a lot in the future. The price may go up or down as those expectations for the future change (a high P/E stock can announce record profits and have the stock go down, if in fact the stock was being priced on the expectation that the profits would be higher than announced).