"Which scriptures are the basis of these claims?"
Physical activities of mere "procedures" cannot define the true form of SannyAsa. If it were true then won't it become the guaranteed way to achieve the ultimate bliss?
To answer your Q, I don't know which scriptures have the basis for this. This is a partial answer :-)
"how is the ideal Sanyasi described in our scriptures?"
Bhagavad Gita describes in good detail in chapter 3, 5, 6 & 18 beginnings. Common perception is:
SannyAsa = [Renouncing Karma] OR [Akarma]
Which is right. But understand that, Akarma doesn't precisely mean "Not doing Karma"; rather, it means "Not doing [certain] Karma". Former is impossible, while latter is possible.
The closest English is Retirement. A wise analytic (SAmkhya) doesn't opt for SannyAsa just because of tiredness, laziness or fear of failure. But he/she is convinced that whatever "I do" is just an interaction of Prakruti's 3 modes; in reality "I don't do anything at all":
BG 3.27 — All Karmas are enacted in Prakruti by  modes/gunas. Bewildered with ego (false identity), [true] self(Atma) believes "I am the do-er".
Why should one worry about worldly matters, when those are not in control anyway! How much ever one pushes to a building, it won't move a bit; then why to push?
Akarma based SannyAsa
If Karma is renounced then automatically its reward is also renounced. This is a very strong argument for everyone to renounce their Karmas or going on the path of Akarma, the conventional form of SannyAsa.
Below are the challenges faced:
- Practicality: It's simply impossible to have a body in Prakruti's 3 modes & refraining from doing any Karma, i.e. complete Akarma is impossible. To sustain a body, one needs to breath, eat, walk, sleep, & perform daily activities. Even just imagining "I don't do Karma" is also a Karma. Hence the SannyAsa based on complete Akarma has to be rephrased as, "mostly generating Akarmas"; in other words "avoiding as many Karmas as possible".
BG 3.4, 3.5, 3.6 — By not starting Karma, '[the state of] not doing Karma' is Not achieved by Purusha(consciousness); and (by) Retirement(complete Akarma based SannyAsa) really doesn't result in way to SamAdhi(Moksha).
— Anyone for a moment doesn't sustain by generating only Akarma; All have to do Karma under control of  modes born out of Prakruti.
— By controlling sense from (doing) Karma, whose mind (still) dwells for senses, such foolish self (mUdhAtma) is called to be under MithyAchAra (worthless efforts)
If one's mind is already retired from sense gratification, then the purpose of SannyAsa is fulfilled. So called "procedures" are irrelevant after that. Usually under influence of Tamas, some believe that the physical "procedures" are necessity. It can be termed as Vikarma.
- Akarma Sanga (Attaching with 'not doing something'): Akarma Sanga happens due to conscious concern towards Akarma. It's a failure in developing "indifference" towards certain matters.
e.g. a point listed is "Strictly observe celibacy". Celibacy has to be neither "strict" nor be "explicitly observable". Both of these might attach one towards "not having sex", which is as wrong as attaching to "having sex"! One is too much concerned towards "not doing 'it', not doing 'it', ...".
This is Akarma Sanga, where a person's focus is deviated from supreme One to "not doing 'it'".
BG 2.47 — You have only power to (do) Karma, not anytime into reward; Let not Karma happen for reward purpose; Let not be attached to Akarma.
Rather celibacy should be a byproduct of one's lifestyle. e.g. A married soldier while on war, naturally doesn't get involved in masturbation or sexual activity. When he is with his wife, he naturally gets involved in such pleasures. In fact, "Sexual pleasure" is never his concern; he is indifferent to sex. That is plain Akarma, & no Sanga. "Sex" is a physical process, let's not associate it with "Celibacy", which is a state of mind.
Karma Yoga based SannyAsa
Akarma based SannyAsa was prevalent during ancient times as well. But practically everyone has to do certain Karmas to sustain self, be it too less. How much less is subjective & personal. Hence, Krishna redefined it as Karma yoga only!
SannyAsa = [Renouncing reward of Karma] or [Karma Yoga]
In Gita, Karma Yoga is also simply called Yoga at many places, because everyone has to do Karma anyways; so prefixing "Karma" is redundant.
Below are few definitions of SannyAsi:
BG 5.3 — O mighty armed, Know him(her) to be always SannyAsi who neither has disliking nor desires; free from dilemma, is certainly liberated from bondage happily.
BG 6.2 — O PAndava, what is said as "SannyAsa", know it to be (Karma) Yoga; Anyone without retiring from vows doesn't become Yogi.
BG 6.4 — Only when engaged neither for senses nor in Karma of all vows, a SannyAsi is said to be elevated in Yoga.
BG 18.2 — Resigning from desire-ful Karma is known as SannyAsa among wises; Renouncing the reward of Karma is called "renunciation" by clever.
As you may see that, true SannyAsa is about being "disengaged from vows" (if any); and not otherwise.
If both are correct, then which SannyAsa should be chosen: Akarma based or NishkAma Karma based?
BG 5.2 — Sri BhagavAna told, SannyAsa and Karma Yoga, both are excellent do-ers; but between them, Karma Yoga is better than Karma SannyAsa (Akarma based).