Corded, Warm-Sounding Noise Canceling Headphones for Office

Ive always found AKG to be warm but no idea about noise canceling

Is corded the only option? Even then, if you like the Sennheiser sound, the Momentum 4 series can be used Bluetooth or wired with a USB C connector at the phone. I find them "warm" but then I suffer from significant high frequency loss.

You would also probably want to tame the low end as the bass is quite strong. Easily done with through the Sennheiser app.

Do you really need Noise Canceling?
 Noise Canceling is great if your on an airplane,a bus,in a noisy restaurant etc..but I’ve never seen a normal office environment where NC was needed...A good pair of over the ear,SEALED BACK headphones should be all you need...
 Based simply on my research,personal experience with Sennheiser & my experience with Topping Amp/Dacs,along with a tight budget requirement right here is where I would start...Get them from Amazon for $150.00 & use them for a few weeks..If they don't work out,send them back & repost with a firm budget..We'll try again...
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Meet the Sennheiser HD 569

The best in class, remastered.

The HD 569 is a closed-back for those needing noise isolation with outstanding sound quality. Powered by Sennheiser proprietary transducer technology and featuring the 'Ergonomic Acoustic Refinement' (E.A.R) design, the HD 569 drives toward audiophile reproduction. Being closed-back, this around ear delivers noise isolation along with a natural tonal balance. Exceptional wearing comfort is provided by large ear cups fitted with plush velour ear cushions.

Sennheiser HD620S -  https://www.amazon.com/Sennheiser-620S-Closed-Back-Headphones-Speaker-Like/dp/B0D38B6XWR