Speak slowly and buy a decent microphone
Today we're bringing President Roosevelt's foreign policy strategy into the modern era. Big sticks aren't cutting it anymore, and if you speak too quietly your microphone isn't going to pick you up.
There are two arms to this strategy, and both of them are aimed at making you sound more authoritative in the workplace. Talent and grit will get you pretty far up the career ladder, but the unfortunate reality of most workplaces is that it's also important to be adept at navigating politics.
How you say something is oftentimes just as important as what you're saying. There's a lot that goes into optimizing how you present a message–far too much for one blog post–but I can at least give two small bits of advice that are easy to implement. The advice is to speak a little bit slower, and invest a bit of money into a better microphone.
The first arm is to slow down the rate you speak at. While there isn't much robust science on the topic of speech rates, this is one of the very first things you'll be told if you ever undergo media training.
In general, people talk faster when they are nervous. The theory goes that listeners are subconsciously aware of this pattern, and are therefore more likely to perceive a fast talker as being nervous and therefore less authoritative. Another aspect which works against you is that speaking quickly will always result in you taking shortcuts with your enunciation. When words aren't spoken clearly it's harder for audiences to understand you, which makes it harder for them to buy in to your vision.
Slowing down your speech solves both of these issues.
A side bonus to this is that speaking slower gives you more time to think about what you're saying. Most importantly that little bit of extra time makes it easier to avoid relying on filler words, and there is robust research that suggests overuse of filler words  is detrimental and cause others to perceive you less favorably.
When Caroline Kennedy was running for the New York Senate, she conducted a live interview in order to give herself a more personal edge. However, because of her extensive use of filler words, she lost much of her credibility. Reporters from numerous publications criticized her and claimed that her use of “cringing verbal tics . . . showed her inexperience”.
You don't want to completely eliminate disfluencies from your speech. Words like "um" and "uh" also play a role in breaking up your speech so that listeners can more easily parse what you're saying. If you're an average person, however, you likely have room for improvement. Frederick Conrad's study on telephone survey invitations pegs the maximum allowable filler rate at 1.28%. For an average sentence of between 15-20 words, you're looking at about one filler word per six sentences before your perceived credibility reduces.
Fortunately, it's easy to work on slowing down your speech. Simply being mindful of your rate of speech in the first place is often enough to make an immediate improvement. Beyond that, there are a number of good strategies outlined at the end of this LinkedIn article.
Buy a decent microphone
The second arm is to invest in a decent microphone. This hasn't been studied in too much detail yet, but I expect that as remote work continues to grow in popularity we'll start to see more interest in this topic.
The current state of the art is a study conducted within the context of online conference talks. The study found that researchers presenting with worse audio quality were were evaluated less favorably than researchers presenting with better audio quality–even when the content being presented was identical.
It's unclear how well this translates over into the workplace, but anecdotally I get a lot of positive feedback on my audio quality. A microphone that's better than your AirPods, webcam, or laptop is surprisingly cheap so I figure it's worth taking a punt.
I use this cheap microphone made by Uhuru. Back when I bought it in July 2021, it cost me NZ$80.31 and came with every microphone accessory you could possibly want. That particular product page is now dead, but it seems like they might still be selling the same product over here now.
I rate my microphone pretty highly–the only issue is that while it bills itself as a cardioid microphone, I find that it still picks up quite a bit of noise from behind. If you don't have a noisy keyboard then this won't be as much of an issue for you.
The theory here overlaps with the one for speaking slowly. Poor audio quality makes it harder for other people to understand you, and people are naturally distrustful of what they don't understand. Unrelated to the question of audio quality a separate study found that when trivia claims were presented with a difficult to read font they were rated as less likely to be true compared to when the same claims were presented clearly.
Another place we can look to is social media: nobody is building their YouTube career off a C920's microphone. Consumers of social media are quite tolerant of poor video quality–there's still a lot of 1080p content out there–but poor audio quality is really grating. Your baseline audio quality is doubly important when you consider that most mobile devices and business headsets have poor speakers in the first place, which will exacerbate imperfections in your speech.
What's the impact?
It's hard to say exactly. Buying a new microphone isn't going to guarantee a promotion during your next performance review–that would be pretty silly. But it might help enhance how your peers perceive you and your work, and it might help you get an edge over another candidate during a job interview. These two bits of advice aren't substitutes for being good at what you do.
A lot of advancement in life is the result of accruing small edges over time. Accumulative advantage is a powerful force that allows companies to scale up into multinational conglomerates that choke off all competition, and the same is true on a smaller scale for you individually. These two bits of advice won't make or break you but they'll give you an advantage, and when you accumulate enough advantages you start winning.