We get this type of question a lot around Availability as being part of the CIA triad.
Defintions
Keep going in your exploration of definitions and look at "Availability": https://www.iso.org/obp/ui/#iso:std:iso-iec:27000:ed-5:v1:en
3.28
information security
preservation of confidentiality (3.10), integrity (3.36) and availability (3.7) of information
3.7
availability
property of being accessible and usable on demand by an authorized entity
Note that it says "property of" not "state of". The loss of the "property" of availability is different from the loss of the "state" of availability.
According to ITIL (which you mention), Availability is:
The ability of an IT service or other configuration item to perform its agreed function when required.
Can you see the logical separation between the two different types of Availability? One is a property, the other is a state/ability. And the infosec and service delivery management processes and goals are different.
Is all Availability the domain of Security?
My reading of the ISO definition is that any loss of availability would be considered an information security incident.
However, the ISO definition would be broad enough to include them.
So, let's take your argument that all Availability concerns fall under the ISMS and are managed by the security department and the ISMS. And let's also consider that we're talking about the management system (ISMS or ITIL) that has the primary responsibility since that appears to be what you are talking about.
That would mean, in this argument, that all Availability Management in ITIL is now a subset of the ISMS. Power, electrical code compliance, operating environment, humidity, static management, network and storage capacity, service load, hardware faults, SLAs, anticipating customer requirements, delivery design, availability reporting and metrics, etc. are now all managed in the ISMS.
First, let's do a sanity check: do you believe that that is what 27000 intended in the definition and in the rest of the document family?
Second, does the rest of the 27000 family support all this activity?
Third, does that mean that only Availability Management in ITIL gets subsumed by the ISMS, or does all of ITIL get subsumed? If only part, why just a part? Are all operational concerns now to be managed under an ISMS?
Fourth, does it make more sense that there are categories of Availability, one related to the security of information and another related to service delivery, even though the wording isn't specific?
Let's test that last one. Let's look at the definition of "audit scope":
3.4
audit scope
extent and boundaries of an audit (3.3)
To use the same broad brush of interpretation, does "audit scope" include the size of the room that is used to conduct audits, as the walls of a room are included in the undefined term "boundaries"?
The definitions in 27000 are very light, as you can see.
So, let's circle back on that sanity check.
The understanding is that there are categories of Availability; one is around security (and can include BCP/DRP) and one is around operations. And that is alluded to in the 27000 definition: "property of being accessible and usable on demand by an authorized entity".
Having the property to be used by an authorized entity is the key differentiation.
A blown capacitor on a network card is an operational concern (i.e. the "ability to perform" (a la ITIL)).
The "property to be used by an authorized entity" (and by extension, not by an unauthorized entity) covers whether systems and information should be accessible. Should that device have a network card? What network should it be on? What access (availability) should it have to other networks and nodes? etc.
So, I go back to my comment: "all poodles are dogs, not all dogs are poodles". Infosec Availability is a form of Availability, but not the sole category of Availability.
Confusions
There are some confusing elements in reality, for example:
- DDoS is a flooding of network capacity: is that a a security concern or an operational concern?
- BCP/DRP is about getting services running again: is that a security concern or an operational concern?
- Secure coding/system design is about building things in a way to meet security requirements.
The reality is that some Availability concerns tend to fall under security because of various side issues.
DDoS is purely a capacity and throttling issue, but tends to fall under Security because Security resources tend to understand the "properties" of the causes and tools to create the problem. But, ultimately, it is an operational issue.
BCP/DRP is often championed by Security, but should not be solely in the domain of security, at all (it's a Management issue, really). But just because security pros tend to be the most experienced in the process of creating and testing BCP/DRP, that does not make it purely a security topic.
Secure coding/system design is monitored and tested by security, but is the domain of the developers and designers. It's not security's job to make those things secure. However, security professionals tend to lead those discussions due to lack of training and knowledge of developers/designers.