Broadcom is doing a leveraged buy-out via debt. So they need some sort of quick cash to avoid being swamped by debt. With that sort of debt load, the short term trumps the long term because if you don't deal with the debt in the short term, there is no long term to worry about.
"How would they force Qualcomm to continue its R&D for 6G even if they stay on their own?"
They don't, but Qualcomm has a good history of ignoring activist investors who call for them to split their chip-making and patent trolling arms.
"How would they know, even if Qualcomm continue its R&D, those tech will be made into 6G standard, and not any Chinese competitors?"
They don't, but they do know that Qualcomm has successfully done so in the past, and that it won't happen if they don't even try.