Welcome to the central absurdity of Common Law.

Where the Statutes are nice and all, but it's the case law that makes up the majority of the iceberg. You can legally construct an argument with the right cherry picking to justify anything, and the court won't give you time to in the moment read up to ensure that what your opponent claims even makes sense.

You may be getting downvote d for seeming unwilling to "read the link" but you have a 100% sound point.

The law isn't worth the paper it is written on until a judge makes a decision on that particular case, which will be heavily dependent on the arguments prosecution and defense both bring. Which all happens after your encounter with Law Enforcement.

However...

I do want to encourage you that the right you do not assert in the encounter with Law enforcement does not contribute at all to an effective defense. Most reasonability tests only weigh what is said in the exchange to the point where you must clearly and unambiguously use certain legal "magic words" to dispel any illusion of muddied waters for the courts.

Think of it as a protocol.

A cop can stop you. You must accept the interruption.

Hello officer, how are you?

If they ask if you know why they stopped you.

"No sir, but I'm sure you're about to let me know."

You must provide identification if requested.

They must provide a reason for stopping you.

If they ask for consent to search the vehicle, your answer is "No, I do not consent. Are we done here? Or is there more I can help you with Officer?"

They should either respond with:
"You are free to go." End transaction.

Or,

They will assert some justification for further detaining you. If they assert the smell of alcohol or drugs, or a need to breathalyze you, you must consent in most jurisdictions. If you do not consent to be breathalyzed there, or suspect their equipment, you are entitled to be transported to a medical facility to do a drug test to confirm or dispute the result.

If you've done nothing wrong, and you've gotten this far you are now playing paperwork chicken with this cop. They have paperwork to fill out, and you do not. On the other hand, cops are largely immune to the pain of paperwork from doing it day in, day out. If you have a phone, I recommend letting somebody know things are getting interesting, so they can echo it to your social circle. Even employers will usually understand this type of thing can happen. You still do not consent to having your vehicle searched. You inform the officer you'd like to call someone to come pick up the vehicle. If your phone is in your pocket, you tell them that and make sure they understand what you are doing, or allow them to get out the phone from where it is stored if they strike you as twitchy. I'd recommend only doing that as a last resort. Try if at all possible to never leave your phone somewhere a cop can clearly access on your person, or observe there is not a weapon hidden ahead of time.

Note:
Miranda doesn't have to happen until you are formally under arrest. Don't jump the gun. DUI isn't confirmed until the test results are in. It's a pain.

After all of this...

"Am I free to go?"

If yes, end transaction.
If no, God help you, the fates do not smile upon you this day. You will have the makings of an excellent harassment case if this continues for more than 24 hours without them either formally charging you with something, or letting you go.

Contrary to popular belief, cops are people too, and likely have an aversion to having their time wasted. If you get a malicious one, then as scary as the prospect is, the system is still people'd by reasonable folks.

ACAB isn't necessarily a given, but they are not your ally. Ever. Dealing with them is one step closer to having your life ruined. So always stick to protocol.

Be courteous.
Follow protocol.
They must justify their actions in an Official capacity.
Make it as easy for them to finish the process.
If you get into a failure state, just do everything in your power to make sure someone else knows.