There already is something that does what you are imagining, but in an even more discrete way: Spire Health Tags. You iron them on to your undergarment. Unfortunately, they are no longer selling them to people interested in biohacking or for non-healthcare reasons. But, they do sell for much cheaper than the retail price, which is ~$50/sensor, on ebay. But, here is the site for more info:
https://www.spirehealth.com/. You could probably recreate them on your own super easily. The technology being utilized is certainly a Respiratory inductance plethysmography (RIP) sensor with bluetooth connection.
Otherwise, I would recommend starting off with a Garmin device. I personally use a Garmin Fenix 6X Pro, which I recommend. There is a new Garmin watch out, with updated sensors, called the Garmin Enduro, however, I do not know how it fares. It just came out within the past few days or so and there are very little reviews on it. I would not purchase a Garmin until you know if the Enduro is solid or not. It should be noted that the oxygen saturation (SpO2) on the Garmin Fenix 6 series can be questionable for some. I personally would not rely on it, but each update makes it better. [No wrist-based SpO2 sensor should be relied on for regular, non-strenuous activities at this point.] Regardless, Garmin derives your respiratory rate through something called the respiratory sinus arrhythmia. It is updated at a high frequency rate, to the point where you would get near-instantaneous alerts, if you set up your own app or configuration. You do not need an ECG sensor for this, and the photoplethysmography (PPG) sensor works great on the Garmin watches, for doing this. An ECG sensor really is not necessarily superior, and there are significant advantages to PPG sensors (like being able to determine the actual blood volume pulse of your capillaries).
Empatica E4 is the holy grail (which I have), but a Microsoft Band 2 (which you can get super cheap on ebay) does pretty much the exact same thing. There is a full working open source API for the Microsoft Band 2 on Github, which works excellently. For what the Empatica E4 is, it is very expensive. You also cannot use it without a direct connection to the internet. Here is a link to the Empatica E4: https://www.empatica.com/research/e4/. In terms of dealing with the internet problem, in my opinion, RADAR-BASE is the best way of dealing with that: https://radar-base.org/.
I also have a Respiban (a chest-worn device with peripheral sensors--but also monitors breathing), which I use in conjunction with the Empatica E4 and Garmin Fenix 6X Pro. But, it is better always to start off with the starter version of the Respiban, the Bitalino: https://bitalino.com/products/plugged-kit-dual-mode-ble-bt
Using my Respiban in conjunction with the Empatica E4, I used machine learning (via journal articles I referenced and re-implemented) to detect stress (both positive and negative) to a 95+% confidence interval. For both the Respiban and the Empatica E4, I utilize Lab Streaming Layer to interface with Machine Learning packages such as Keras.
But, for starting out, either the Garmin Fenix 6 or the Garmin Enduro will be the way to go.